That's where things start getting a bit difficult to answer.

A 1/2" marble has a horrible ballistic coefficient, which makes it shed its velocity very quickly. On top of that, the marble doesnt have much penetration at those speeds. It's kinda like getting hit with a fastball. A 90 mph pitch carries a whopping 85 fpe, enough to leave a bruise, but not normally lethal. A .22 bullet shot from 75 or so yards away will have similar energy and definitely penetrate into the body and have a good chance of being lethal.
Since you are limited in both velocity and energy, you might want to look into other types of ammo that offer better penetration. Small homemade arrows or darts are probably going to be your best bet for taking down groundhog sized game with less that 6 fpe. You'll want a broad cutting surface to open up as large a wound channel as possible so the animal will bleed out quickly. I'm thinking along the lines of a 1/8" cold steel rod with a 1/2" broadhead made of 12 gauge steel. If you use a 1/2" type L copper barrel, you can use a foam earplug as a stabilizer. Here's a page that shows a dart similar, just without the broadhead:
http://www.airgununiverse.net/darts.html.