
downerbeautiful |

Korada is legal as he shows up in the inner sea world guide, I don't believe Lythertida is legal for PFS as she appears to only show up in the Chronicles which have been replaced by the guide.
Lythertida appears to be legal. Chronicles of the Righteous, page 1, 18. Inner Sea Gods, page 322.
Korada is also legal. Chronicles of the Righteous, page 1, 17. Inner Sea Gods, page 322.
According to Additional Resources, the deities found in Chronicles of the Righteous are still legal; Inner Sea Gods did not replace them as far as their "legal content" is concerned.

Half Brick In a Sock |

According to the GTPSOP, however, only* clerics of Irori get the feat Improved Unarmed Strike (if that's something that matters to you).
*only in regards to free weapon proficiency. Other classes or other deities would require you to select the feat to insure your strikes do not provoke.
In regards to Clerics, yes.
In terms of WarPriests, any Deity with favored weapon Unarmed Strike will grant Improved Unarmed Strike. Lythertida and Korada are both legal, as downerbeautiful notes. There are no others as far as I can tell; I think the list in Inner Sea Gods is comprehensive.

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I think the list in Inner Sea Gods is comprehensive.
I don't know about those with unarmed strike, but I just wanted to respond to this statement. There are PFS legal deities that aren't in Inner Sea Gods. Because that book only focuses on the Inner Sea region, the Tien gods aren't included. Look to the Dragon Empires Gazateer or Primer for those.