Here is a site with a whole host of songs translated into Latin by one Meredith Minter Dixon. Including for example, Blowing in the Wind and its companion piece, Puff the Magic Dragon - Carmina Popularia

While hunting around to find this I came up with another gem, which isn't immediately relevant, but I thought I'd pass it on here - it's a Gilbert and Sullivan version of Xena, Warrior Princess, by Kevin Wald. Here is a taster:

I am the very model of a heroine barbarian;
Through Herculean efforts, I've become humanitarian.
I ride throughout the hinterland -- at least that's what they call it in
Those sissy towns like Athens (I, myself, am Amphipolitan).
I travel with a poet who is perky and parthenian[2]
And scribbles her hexameters in Linear Mycenian[3]
(And many have attempted, by a host of methods mystical,
To tell if our relationship's sororal or sapphistical).

It deserves to be given a proper production.