Methylates the 2'-O-ribose of nucleotides at positions 32 and 34 of the tRNA anticodon loop of substrate tRNAs. 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 Belongs to the class I-like SAM-binding methyltransferase superfamily. RNA methyltransferase RlmE family. TRM7 subfamily.