Amulets have the protection kind of slot to them so I could see allowing it either "at price" or at a 1/4~1/2 cost mark up. A cloak of protection could work at price too since several cloaks are defensive in nature (cloak of resistance, cloak of displacement for example). In a similiar vein I would allow a cloak of invisibility for the same price as the ring of the same since it's just as iconic in literature.
Overall the biggest thing you need to watch for is the "scam" placement of items. If the slot they want to place their "alternative" item in is one that generally houses the same sorts of items and it's not simply a different bonus type of an item that already exists for that slot then sure go for it. They are still using up item slots and paying for the item.
Remember that a large part of the pricing of magical items is an art form not just a mathematical equation... if you feel that it doesn't fit the mold for magical items either don't allow it or increase the base price by a percentage. If it works for you and is in an appropriate slot go for it at base price simply to keep things running smoothly.
If you want to allow it at base price but don't want the practice to be regular make them go on a quest or do more research (eat more time) figuring out the non-standard method for doing what they want.
3.5 had rules for "body slot affinity" which Pathfinder seems to have removed. So, since the fine folks at Paizo removed them, I am lead to believe that not only is this possible, but it doesn't cost any extra when making custom items.
This doesn't bear out with pre-created items (compare boots and helm of teleportation), which reflects the 1.5 times cost for changing a body slot. They did keep the rule for making something slotless (double the cost) and the rules for stacking effects on a single slotted, non-armor items (half again the cost of the lesser addition).
The craft DC should not change and (even in 3.5 in this case, since amulets were for protective magicks) the cost should not change.
I had the same problem with one of my pc's, he wanted to buy a "vest of resistance" to take up the chest slot rather than the shoulder slot that the cloak of resistance offers
same bonus just different slot, I allowed it because 3.5 had the vest in the DMG
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I charge a 1.5x the price for an item in a non-aligned slot.
I now have a paladin with a belt of strength and gloves of dexterity. In the PFRPG core rules they would both be belts, forcing the PC to choose which stat they want to increase and increasing the relative value of unslotted items that boost either of those physical stats. So the paladin's gloves cost him 1.5x the normal price for an item that boosts Dex by the same amount.
If you don't charge extra for items in a misaligned slot, it becomes a race to see how many stat increasing items can be created in different slots. Fortunately, by RAW and RAI items that boost the same stat wouldn't stack anyway as they are all enhancement bonuses so perhaps allowing multiple boosts in different slots isn't a big problem unless: the PC has a single item that boosts multiple abilities at once, or has items that add a bonus other than "enhancement" (competence bonuses are popular for skill checks, for example).
Actually, azhrei_fje, your player's paladin can have a strength and dexterity boosting belt. It's even statted up in core. It's essentially the "two abilities on one item" pricing. 4,000 (base for strength) + 6,000 (base for dexterity x1.5) = 10,000 (belt of physical might). It comes out to the same price as belt of strength and price adjusted gloves of dexterity, and saves you an item slot.
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Actually, azhrei_fje, your player's paladin can have a strength and dexterity boosting belt. It's even statted up in core. It's essentially the "two abilities on one item" pricing. 4,000 (base for strength) + 6,000 (base for dexterity x1.5) = 10,000 (belt of physical might). It comes out to the same price as belt of strength and price adjusted gloves of dexterity, and saves you an item slot.
You would split them if you didn't want to pay the big bucks for the higher boost. So perhaps a +4 DEX belt and +2 strength gloves, which would be less expensive than the +4/+4 belt.
If one of my players wanted something that duplicates a core item in a different slot I would probably charge 50% above the core cost, depends on the item and why the player is doing it.
Well, in the case of a +2/+4 belt, you just use the stacking rules. 18,000 for the +4 item and 6,000 for the +2 item. Still saves a slot. Unless your GM doesn't allow custom items, or the ability to combine items, then this whole discussion is sort of moot.
This has actually been a problem in my games. Essentially magic item creation is now only 3 feats: Arms+Armor, Rings, Wondrous.
"What do you mean Immovable Rod? This is an Immovable Stick! There's nothing saying I can't make a slotless Wondrous Item that does that, right?"
The pricing gets funky, but we're in a setting where we can't purchase any items, it's all self made. So this is letting people get items that would have been impossible without extra feats.
We even had a few party members do that exact same "ring of shield" trick that the OP described.
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This has actually been a problem in my games. Essentially magic item creation is now only 3 feats: Arms+Armor, Rings, Wondrous.
"What do you mean Immovable Rod? This is an Immovable Stick! There's nothing saying I can't make a slotless Wondrous Item that does that, right?"
The pricing gets funky, but we're in a setting where we can't purchase any items, it's all self made. So this is letting people get items that would have been impossible without extra feats.
We even had a few party members do that exact same "ring of shield" trick that the OP described.
Custom magic items are essentially house rules. If a character wants to craft something then the GM needs to evaluate how it's going to impact the game and make a judgement call on pricing and whether it should even be available. If you feel a custom item isn't reasonable then say no. There is a reason those are called guidelines and not rules and why they say "These are a starting point...".
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Scrolls, Wands, and Potions are pretty clearly their own thing. Single use caster, multi use caster, and single use anyone respectively.
I'm not sure I would break it down that way (the way you did) but the current way is somewhat arbitrary. Body slots aside it's not quite clear what makes something a ring or a rod or a wondrous item.
I don't believe in letting players cheese out of requirements. In fact I generally require that if a player wants to create an item that has a form of another item type, say a Rod of Fire, BOTH Feats are required for such a task.
The reasoning? If you're going to take an established item form and change it, you need to know the basic form first before you can alter it.
Your PC has some hard choices to make and that's part of the game.
That's probably how I would run it as well.
I don't allow players to make rings into different slots without a good reason or them paying a lot for it. The primary reason is that rings have to be different from wondrous items in order for them to be useful at all. Moving around wondrous item slots aren't that bad because you have plenty of them anyways, but you only have two ring slots, and if you can make them for some other part of the body instead it makes them kind of useless, as well as forge ring kind of useless when you can just be making wondrous items instead.
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I find the distinctions between item categories poorly made right now. I was thinking of rewriting the basic item creation feats to be something more along the lines of:
Craft Spell Completion
Craft Spell Trigger
Craft Continuous
Craft Use Activated
Craft Command Word
Craft Enhancement (anything where you use magic to enhance normal function without in any way replacing it, ie weapons and armor)
Craft Charged (to allow more than single or infinite use as choices)
etc
For example, a Rod of Metamagic would require Charged and Use Activated. A potion would require Use Activated. A weapon's base enhancement would require Craft Enhancement, but command word activated specials might require Command Word. Makes certain things more special. Oh, and a Wizard would start with Craft Spell Completion (which allows scrolls by itself).
For now I just allow a player to create anything they can justify reasonably (sans discounts, I made those separate feats and DM fiat only).
A ring is special because you can place anything on a ring without regard to affinities, but other than that I see no reason to restrict it.