The information below was provided by Daniel Mikola, who I thank most profusely for doing such in depth research.

A forum post concerning an interview with Composer Joel Goldsmith began my search for you:
Gilles Nuytens: Could you let us know about your studio session with Rachel Luttrell (Teyla) for the song "Beyond The Night" featured in Critical Mass?
Joel Goldsmith: When Brad asked me to write the song for Teyla, I happened to be working with my sister Ellen on a children’s album she was recording. I thought it would be fun to write the song with Ellen. The writers of the show had supplied us with the lyrics and Ellen and I wrote the music. Brad sent Rachel down to our studio in Los Angeles to record her vocals. I was pleasantly surprised at what a skilled singer Rachel  was and it made my job so much more enjoyable. But what was the most fun was having “Teyla” in the studio! After she finished recording the song, I told her, “You know, you don’t look sotough to me!”, she then grabbed a violin bow and proceeded to kick my ass with it! Ok, maybe that didn’t happen, but the part we had a great time and she did a great job was true. Rachel is a very nice person and I hope to work with her again one day.

Story for that episode was by Brad Wright and Carl Binder, while another forum's post credits solely Carl Binder:
Rachel Luttrell makes her television singing debut in this episode with a song ("Beyond the Night") composed by the late Joel Goldsmith and his sister Ellen, with lyrics by Stargate's own Paul Simon = Carl Binder.