Berman's Rainbow Dreamers was a 20th century Earth group, popular during the 1960s.
Berman's Rainbow Dreamers performed at the Behr Theater in San Francisco during the summer of 1967. (DS9: "Past Tense, Part II")
The poster featuring the performance was in the background during O'Brien and Kira's brief appearance in the 1960s. The date is derived from the script, which described it as the "Summer of Love". The band's name is an homage to executive producer Rick Berman. (Star Trek: Deep Space Nine Companion, pp. 201-202)