what is the easiest way for me to do this? I tried drilling it out with a drill press and it came out like s**t.
Ignoring the scale for the moment, the way you'd traditionally approach something like this* is 1) excavate the bulk of the material, 2) flatten the bottom of the recess, 3) clean all four edges up and then 4) do any final flattening of the bottom that's needed. Steps 2 and 4 would generally have been done with a hand router where the bottom needed to be particularly flat and clean, if that wasn't needed you could just scrape to flat(ish) using the edge of the chisel.
In many cases step 1 above would have been done by drilling to depth using a suitable bit (these days a Forstner or sawtooth bit would be most commonly employed, back then usually a centre bit). All three of these bits will leave dimples from the central lead screw/point on the drill bit, but that's not a big deal on a non-show surface.
So drilling away a good bit of the waste is actually a good way to approach this sort of thing, the small size is probably what gave you trouble. The smaller you're working the more careful you have to be in a relatively coarse medium like wood because just one errant splinter can ruin the piece you're working on, where on a full-size table leg that same size of splinter might barely be noticeable.
Now because this is so small you can quite easily accomplish the task entirely by chiselling (after careful marking out of course). But if you need the recess to be very neat and the finished size very accurately 1/2" x 2" I would strongly recommend not using a 1/2" chisel. An expert could, but you are virtually guaranteed to end up with irregular edges no matter how careful you set out to be and these would need to be trimmed back to neaten up so you'll end up wider than 1/2". So if you do this with a chisel it would be preferable to use a 1/4" or 3/8" chisel for the excavating work, then trim the 2" edges back to your knifed layout lines with a 3/4" or 1" chisel (not essential but a wider chisel = fewer cuts = better chance at a cleaner result).
In case it needs to be said the chisels should be very sharp for this — as chisels should always be — so if necessary hone them or strop them immediately before starting. Chisels only work properly if very sharp and although it seems paradoxical they're safer to use.
Also make sure the workpiece is held firmly to work on it! Presumably there'll be a vice of some kind in the co-op workspace so do make use of it, with the jaws padded using folded paper or card if necessary to prevent bruising of the maple.
*For example cutting the recess for an oilstone box to receive the stone, see links in previous Answer.