Are there any fully working Apple II emulators for MorphOS? At the moment I am using ApplePC on DOSBox which runs full speed on my G5, but I'd rather use one right from morphOS if possible.

Yes there is. It's Basilisk II and you can find here:
http://morphos-files.net/find.php?find=basilisk
I can't tell if this is the best Apple II emulator for MorphOS since I've never used but it seems to be well done and with very good features. Pros: it is native, uses MUI and AHI. Cons: use full speed. Anyway I guess it's worth trying it

Edit:
I'm using a little and it's not that bad! I found others Apple ][ emulators on Aminet but not really exciting discovers...

Isn't Basilisk II a 68k Mac emulator and not an Apple II emulator?

Whoopsy! It seems I made a "Type mismatch error" . Yes Basilisk is a 68k emulator...
Maybe you could try this:
http://aminet.net/package/misc/emu/SDDapple-MorphOS

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I saw that, but it seems to be an early beta with no sound support. No go

MESS probably supports it, no idea how well though...

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Hmm, I never even gave MESS consideration as I've never really followed it. If the morphOS version is as complete as other versions, it looks like Apple II is supported with good emulation.

Thanks for the suggestion. I will try it out tonight!

after you try it out..post up.. I'm intersted to see what you think. I'm still reinstalling all of my old software on my G5 so I wont have time to mess with it yet.