Stalemate rhymes with:
schoolmate, acclimate, amalgamate, automate, breakmate, checkmate, classmate, decimate, dichromate, glucosamate, glutamate, inmate, multimate, overestimate, papermate, phonemate, playmate, primate, roommate, schoolmate, shipmate, shoemate, shumate, teammate, underestimate, unimate
Stalemate sounds like:
scotland, settlement, shadowland, shetland, sidelined, southland, stalemated, swedlund, sweetland, swetland