All of the following resources can be helpful in identifying plays that meet specific criteria. They vary in terms of how much granular control they give you, as well as in the body of plays searched.
Discover plays by applying filters (genre, major themes, time period, cast, playwright attributes, awards, etc.). Results reflect the print holdings of UC Irvine's library; to find a play at Watzek, take the title you're interested in over to Primo.
From UC Berkeley's department of Theater, Dance, and Performance, "a website dedicated to BIPOC (Black, Indigenous, and People of Color) playwrights of the 20th and 21st centuries, whose works are in English or with English translations widely available."
IBDB (Internet Broadway Database) archive is the official database for Broadway theatre information. IBDB provides records of productions from the beginnings of New York theatre until today.