Do you want this for music or for sound effects?
For sound effects, the Game Boy actually has a wave channel (if you've played
Pokémon Pinball, you'll recall the "Pika!!" sound effect was literally a recording of a human voice actor... so that's how they did that). I'm not too familiar with how it works, but from my limited understanding I think it can play wave files granted that the wav is very short and low-quality: a maximum of 32(?) samples at 4-bit bit depth, at a sample rate of 11.468 kHz (I think that's the sample rate... I got that number from
here, from
here).
So I believe if you use Audacity, you can just change some of the settings before recording the sound effect, and then when you record it the quality would probably be pretty close to what's on the Game Boy.
I also found this ROM:
GB SFX Generator - Not exactly what you're looking for (it doesn't convert recordings to GB quality), but the sounds are made using the GB hardware (or emulator), so they're authentic.
For music, I'd recommend a different ROM called
LSDJ (you need to pay a small donation, but it's well worth it). LSDJ is very popular among GB chiptune composers. And I haven't done this, but I think there's some way to import 4-bit wav samples into LSDJ as well (so that they play on the Game Boy / emulator).
Some other music-related ROMs I've come across are:
chord and
Pixelh8 Music Tech V2.0. Probably not too useful, but I thought I'd post them.
edit - Also, if you're planning on using these for a Game Boy styled game, I'd recommend learning a little about how Game Boy sound works. Basically, the Game Boy has four sound channels: two pulse channels (good for musical notes and certain kinds of sound effects), a wave channel (good for instruments or recorded sound effects), and a noise channel (sounds like whitenoise, or kind of like TV static). All four channels can play at the same time, but each channel can only play one thing at a time. So if your music uses all four channels and you want to play a sound effect on the wave channel, you'll need to temporarily mute the music's wave channel in order to play the sound effect.
Download Famitracker. It's a music/sound program to create music and sound effects that can actually run on real NES hardware, and you can add your own short samples to use as "instruments". It's not Gameboy, but it's the closest thing I can think of.
There's a program called
Game Boy Tracker which seems to be the Game Boy equivalent (not made by the same people though). I haven't used it, nor have I used FamiTracker, so I don't know how the two compare.