I found the meaning in English is to "cherish" and the meaning in French is "darling." Which makes sense when you look at the southern Creole language; they use "Cheree" as a term in endearment. "My Cheree:" my darling. My nickname is Reese, Reesie, Reesey, the list goes on. :-)
I do not think that the best explanation for Cherice and Cherise is that they are variations of "Cerise". Instead I believe that they are spelling variations of Charisse, the surname of the Hollywood star Cyd Charisse. Charisse, Charise, Charice, Cherice, Cherise, Chereese, etc. seem to date from the time Ms. Charisse was famous. Her surname came from her first husband, Nico Charisse, her dance teacher, who was himself a son of Calliope Charisse, a famous dance teacher in France who was of Greek descent. It seems most logical to assume that Charisse is a "Frenchification" of the Greek word "charis" and so Cherice and Cherise are more related to Charis and Charissa than they are to Cerise. [noted -ed]