I sing parodies of tons of songs, and, "Blue Moon" is in the top tier. But it's never a full parody, it goes like this, every time:
Bluuuue MOOOOOOONNNN, you saw me ____ (often is "standing" or rhymes with it) [on] a ____ (if it's not "hill," it's the other thing I see or am doing).
Also, a few times a day, it's just like this:
Bluuuue MOOONNNN, you saw me feeding both the cats
Snowball is getting kind of fat
Flashie, stop eating out of thaaaaaat [Flash gets in the sink]