Arquette's talent attracted praise from Cox's A-list friends.
Marriage Story star Laura Dern commented "GORGEOUS Coco."
Kate Hudson wrote: "Oh honey, her voice!"
I, Tonya actress Allison Janey gave her verdict, writing that she sounded "beautiful".
Others joked about her apologising for cursing before launching into a lyric of a song.
"'Sorry I'm cursing' what a sweetheart!" commented Tan France from Queer Eye.
The actress and her daughter have previously showcased their mother-and-daughter talents by filming a dance on TikTok together.
Jennifer Aniston is Coco's godmother.
Last month, a Friends reunion special was confirmed. Cox, who played Monica on the hit sitcom, is reuniting with the rest of the main cast for an unscripted special.
Cox told Kevin Nealon, host of the webseries Hiking with Kevin, that she is "so excited" for the reunion.
"So the exciting thing is that we're all going to get together for the first time, in a room, and actually talk about the show," she told Nealon.
"We're going to have the best time. It's going to be great."
The special is screening on new HBO streaming service HBO Max, and there's no word yet on where it will be available for New Zealand audiences.
The Friends reunion will be available when the service launches in May.