Catalysis of the reaction: adenosine37 in tRNA + 2 reduced - + 2 S-adenosyl-L-methionine = 2-methyladenosine37 in tRNA + 5'-deoxyadenosine + L-methionine + 2 oxidized - + S-adenosyl-L-homocysteine.
tRNA (adenosine(37)-C2-)-methyltransferase activity