Hi there..
So sweet of you to find a Birkin for your wife..
Rose Jaipur and Rose Lipstick is very similar, RJ has more coral while RL is more pinky but still has some coral tone on it.
RT is deep pink.. Its the prettiest pink IMHO, but RT only comes in Epsom leather.. And im not a big fan of epsom.. RJ comes in Clemence and Epsom.. Am not too sure about RL i think it comes in either Togo or Clemence..
I personally would go for either RJ or RL in GHW.. I think its easier for you to get RL since its this season's color while RJ is from last season..
Good Luck..