Your best bet would be a Retrobit SNES to GBA adapter and a Super Gameboy on a SupaBoy or Retro Duo Portable. The GBA adapter doesn't play on the SupaBoy system like a Super Gameboy, but if you use the adapter wire, it works on a TV, and the SNES controllers are a great way to play GBA games, since the controllers are easier to handle. The GBA adapter is designed to work on the Retro Duo Portable, so it works on the system, with a better screen, from what I've seen. I only have the SupaBoy, and neither option works for Gameboy Color games, but it's cheaper than a Gamecube & Gameboy Player combo. That, plus the Retrobit NES,Genesis, and Famicom adapters (made by the same Chinese manufacturer) all work on most SNES systems, even clones, so it's a REALLY great option, TV or handheld.
Any new developments on this? As far as I can tell, a gamecube + GBPlayer is still the best way to go. Am I wrong?
No, you're exactly right. The only hardware solutions are GBA, DS/DSL and GBP, everything else is just emulation. Iirc there's a TV out mod for the GBA, so that might be another option, but the necessary hardware isn't readily available (any more) afaik and I have no idea about the video quality. Probably doesn't have that slight timing/stuttering issue the GC/GBP combo has though, I would think. edit: Actually, there's this car DVD player thingy with integrated GBA, that might be an even better option. But good luck finding one of those.
That Advance Game Port = adapter to read carts, games are then running in software emulation. Even says so on the wiki page. Emulation is usually not what you want, especially if a tird party (in this case Datel) wrote it. And if you're OK with emulation, just use a PC, maybe with a bunch of gaudy upscaler filters. GBP Stuttering: http://assemblergames.com/l/threads/gameboy-player-pcb.27687/#post-573957 Haven't noticed it myself, but then again my eyes aren't the best.