I did a search through my Georgian CD collection and found the following renditions of Suliko:

Batonebo/Ensemble Kakheti
Pan Records, 1993
sung by the Kakheti Ensmble (men)

Georgie/Ensemble Aragvelebi
Planett/WMD, 1993
sung by the Ensemble Aragvelebi (men)

Soinari/Folk Music from Georgia today
Haus der Kultur der Welt, 1993
sung by Mzetamze (women)

Georgia/The Resounding Polyphony of the Caucasus
Music of the Earth/Multicultural Media, 1997
sung by the Telavi Ensemble (women)

None of the above are guaranteed to be still in print or available, although--

Perhaps the best way of obtaining something is to do a "song search" on Amazon.com., which brings up most of the above, and the last two of them are still listed as available. Most of the other amazon.com listings are actually by Russian or Soviet performers.

There are more versions on my Soviet-era vinyl LPs from Melodiya, but the song was overdone in the the past and seems to be taking a well-deserved rest in relative obscurity in the post-Soviet (and now CD) era.

--Charlie Baum