Using the guidelines for Estimating Magic Item Gold Piece Values for a ring of divine favor +3 gives a price of 72,000 gp (spell level 1 x caster level 9 x 2,000 gp x 4 for a spell duration measured in rounds). Does that seem right to you? It seems to compare reasonably with an amulet of mighty fists +4 (80,000 gp), given that it gives its bonus to any attack and weapon damage rolls, and it's a bonus type (luck) that will stack with many other standard attack and damage bonuses.
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Leaving aside the question of "should this item be allowed?" for a moment. . .
That pricing tracks for making a magic item that duplicates a spell. However, for this particular item, I'd price it more like the other items that provide numerical bonuses. (Ring of Protection, Amulet of Natural Armor, Amulet of Mighty Fists, Headband of Vast Intelligence, Weapon Enhancement bonuses, etc.) All of which follow a price formula of
(bonus squared) * X
Where X varies depending on what exactly the item does. Trying to work out this item using that standard.
Start with an enhancement bonus for a weapon being Bonus^2 * 2000. An amulet of mighty fists (which can apply to multiple attacks at once) is Bonus^2 * 4000. I'd double the price again since your ring is providing a bonus of a type other than enhancement (compare Ring of Protection to enhancement bonus on armor). So we end up with:
Price of Ring of divine favor = (bonus squared) * 8000 gp.
Hey, that works out to exactly the same price for a +3 ring! (But makes lower bonuses cheaper.)
"Should this item be allowed?" You always have to be careful when adding an item that provides a bonus type other than enhancement. You don't want people stacking up 5 different types of +1 bonuses for less than half the price of a +5 enhancement bonus. I'm actually OK with the +3 ring, and probably a +2 as well. Even though the always-on attack and damage bonus is very nice to have, it's quite expensive. But I wouldn't allow a +1 ring.
You always have to be careful when adding an item that provides a bonus type other than enhancement.
Yup, especially if it's a luck bonus that gets boosted by the already very strong Fate's Favored.
And I'd rather compare it with an amulet of mighty fists, like Callum did. A divine favor ring would offer both a boost to attack bonus and damage in a single item - slots are a precious resource, after all. And the type is unusual, as already pointed out. Finally, it works for any attack, not just natural attacks. So 72k make sense, even though it seems much first.
I probably wouldn't allow it on the first place, tbh.
A +3 to hit and damage that stacks with everything?
Worth mention, divine favor's duration is 1 minute, not rounds.
But 72k is going to keep it out of the realm of low level play, and by high level players are almost certainly going to have access to worse things.
I still wouldn't allow it except in an unoptimized party for a character who was really struggling to keep up, or in a no-holds-barred cheese fest.
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Personal spells like Divine Favor are designed to be less accessible than regular spells like Bull's Strength. It's there to make it possible for a Cleric to participate effectively in battle (at the price of a Standard action and a spell slot) despite having lower BAB than a full marital.
Allowing personal spells to be attached to an item gives that power to people who were never intended to have it, and should be priced appropriately or banned.