CFG to generate $L = \{a^{2n}b^n\} \bigcup \{a^mb^{2m}\}$
In this case you have the union of two trivially CGF languages and usually that is achived by the following trick. You write some $S_1$ grammar for the first one, $S_2$ grammar for the second one and just "or" them somewhere at the top level (here it's $S$). Your approach was just to use single recurrent literal, if I can say like that, and thus it was difficult to come up with CGF rules. 

You would get something like this:


   $S \to S_1 | S_2 $

 $S_1 \to a^2 S_1 b | a^2 b$

 $S_2 \to a S_2 b^2 | a b^2$