
Ipslore the Red |

Use the spell Vanish. Level 1, CL 1, duration in rounds/level so multiply the cost for a continuous item by 4. Spell level*CL*2,000*4 gives you 8,000 gp.
Use regular Invisibility. Level 2, CL 3, duration in minutes/level so multiply the cost for a continuous item by 2. 2*3*2,000*2 gives you 24,000 gp.
Vanish would be cheaper and easier.

Fuzzy-Wuzzy |

I believe Ipslore and Robert's calculations would apply to a magic item that could turn YOU invisible continuously. An item that just turns itself invisible should be a very small fraction of that. I'm going to say around 500 gp---call it 400 gp by itself or 600 gp as an add-on. But I wouldn't argue with someone who wanted to make it even cheaper, as I have nothing solid to back it up.

Fuzzy-Wuzzy |

You are still replicating the invisibility spell, so you must calculate based on that spell.
Except the calculations you reference are just guidelines. You're supposed to adjust for the item's actual usefulness. Generally this is seen at the other end, with the guidelines pricing something way too low for what it gives you, but it applies the other way too.
Not all items adhere to these formulas. First and foremost, these few formulas aren't enough to truly gauge the exact differences between items. The price of a magic item may be modified based on its actual worth. The formulas only provide a starting point.
An example would be dull grey ioun stones. They float around your head continuously, but their price reflects neither continuous fly nor continuous levitate. Floating ITSELF is so cheap that they don't even bother to factor it in to the costs of any other ioun stones.

Robert A Matthews |

They are guidelines that many items in the book use to come up with a balanced price that stays pretty consistent. Yes there are exceptions, but the exceptions are still pretty close to the effects they replicate. The guidelines are there to be used, not ignored. If you are trying to create an item that exactly replicates the effects of a specific spell, it only makes sense to use the formula for placing that spell on the item. For the record, ioun stones don't entirely replicate the fly or levitate spell. You can't make them fly anywhere except around your head as they orbit 1-3 feet above you. Also, flying is not invisibility so we are really talking about apples and oranges here.

blahpers |

This is an expensive ability. Compare the Paizo blog's (unofficial) writeup of an intelligent item with the Hiding ability. This only allows affecting itself as the spell once per day, and they price it at 1,200 gp. Furthermore, it disables any active abilities on the object. Having a permanent effect and retaining the other abilities of the item more than outweighs the lost utility of being able to turn the effect on and off.
This is difficult to price. I would probably cap the cost to create an item with this effect at cost of a permanent invisibility spell, which is 5,000 gp. So that would be a market value of 10,000 gp. Depending on the item, I could go down from there. An invisible marble ought to be easier than an invisible wagon.
Note that vanish is intended for use on creatures only, so I don't think it'd be a good guideline.

Fuzzy-Wuzzy |

They are guidelines that many items in the book use to come up with a balanced price that stays pretty consistent. Yes there are exceptions, but the exceptions are still pretty close to the effects they replicate.
A ring of continuous mage armor ought to cost 1 * 1 * 2000 = 2000 gp according to the particular guidelines you're using for invisibility.
Any GM who doesn't adjust this to the 16,000 that bracers of armor +4 cost is screwing up. I don't consider a factor of 8 to be "pretty close."The guidelines are there to be used, not ignored.
While this is true, it is not an excuse for treating the guidelines as rules.
If you are trying to create a spell that exactly replicates the effects of a specific spell, it only makes sense to use the formula for placing that spell on the item.
See above re mage armor. It makes sense to start with the given formula. It does not make sense to insist on stopping there. You're not giving any discount for the OP's fundamentally underpowered request of a ring of only-turning-itself-invisibility. Heck, you're charging him more than an actual ring of invisibility costs!
For the record, ioun stones don't entirely replicate the fly or levitate spell. You can't make them fly anywhere except around your head as they orbit 1-3 feet above you.
Yes, they get a rather limited version of fly. And the OP wants a ring (or whatever) with a rather limited version of invisibility.
Also, flying is not invisibility so we are really talking about apples and oranges here.
Um... why would the issue of pricing an item that could fly and the issue of pricing an item that could turn invisible be radically different?

Robert A Matthews |

Well, permanency can be cast with invisibility on objects, so that is an official way. 5000 gp plus paying the caster (less than 1000 gp), but it is susceptable to Greater Dispel.
Are there any rules for using e.g. invisible weapons?
This is a much better way to go about it, didn't even occur to me. So 5060 GP for an invisible item.

Ipslore the Red |

Well, permanency can be cast with invisibility on objects, so that is an official way. 5000 gp plus paying the caster (less than 1000 gp), but it is susceptable to Greater Dispel.
Are there any rules for using e.g. invisible weapons?
The only precedent is Baraket, the (major artifact) Sword of Pride. The effect specifically associated with its blade's invisibility is a decent bonus to feinting.