Try JPEG 2000 Quicktime for maximum compatibility. Set quality to about 90 or 95.
That's probably the best 8bit codec right now for general distribution. Another good 8bit codec under QuickTime is GoPro Cineform. Very pleasing results for an 8 bit codec.
If you need higher bit depth there are 3rd party codecs that support alpha channels and 10 or more bit color depth.
Is the JPEG 2000 Quicktime a video format? Also what kind of 3rd party codecs are you talking about?
If you're on a Mac with FCP installed, you could go with ProRes 4444. But you have to understand that ANY kind of file that supports and alpha channel is NOT going to be small.
JPEG 2000 is available under QuickTime>Formats. It is a very good 8bit codec. Don't expect file sizes that are close to h.264, but expect 8bit, visually lossless, frame based with alpha channel support. Just open up the render cue, then click on the output module and select QuickTime>Format Options. You'll find JPEG 2000 there. Pick the format first then set the output module to RGB+ Alpha, Millions+ and Alpha to STRAIGHT -- please don't ever send anyone a pre-multiplied alpha.