Unimate rhymes with:
acclimate, amalgamate, automate, breakmate, checkmate, classmate, decimate, dichromate, glucosamate, glutamate, inmate, multimate, overestimate, papermate, phonemate, playmate, primate, roommate, schoolmate, shipmate, shoemate, shumate, stalemate, teammate, underestimate
Unimate sounds like:
uinta, unaided, unamended, unanimity, unaudited, und, undated, undid, undo, undue, unedited, unheeded, unimedia, uninitiated, unit, unita, unite, united, unity, unmade, unmanned, unmet, unnamed, unneeded, unted, untidy, untie, untied, untiedt, unto, unwanted, unwed, unwind, unwound