Catalysis of the reaction: cytidine(32)/guanosine(34) in tRNA + 2 S-adenosyl-L-methionine = 2'-O-methylcytidine(32)/2'-O-methylguanosine(34) in tRNA + 2 H+ + 2 S-adenosyl-L-homocysteine.
tRNA (cytidine(32)-2\'-O)-methyltransferase activity