Swami Vivekananda mentions :
in Western language, a man gives up the ghost, but in our language a man gives up his body. (CW).
So people in the Western Coutries identify the individual with the body of that individual which is buried. So there is the conecept of RIP.
The Hindus, when one dies, say that he or she has given up the body (deha-tyAga). So they cremate or burn the body and then do the srAddha rituals for the peace of the soul. It is believed that srAddha ceremony, if properly done, pleases the pitris and the God and the departed soul is able to move to heaven and enjoy bliss there.There is the notion of rebirth also.
So there is no concept of RIP in hindu culture.
The substitute of the wishful word is 'SvadhA' which means
sweet libation, oblation to the Manes (sanskritdictionary.com)