Green’s Dictionary of Slang

browning sister n.

also b.q., browning queen
[browning n.1 (1) + queen n. (2a)/SE sister]

a homosexual; in pl., a generic term for homosexuals.

[US]‘Dean Stiff’ Milk and Honey Route 201: Browning Sisters – The Angelina sorority. ‘He belongs to the Browning Sisters’ or ‘to the Brown Family’.
[US]G. Legman ‘Lang. of Homosexuality’ Appendix VII in Henry Sex Variants.
[US]‘Swasarnt Nerf’ et al. Gay Girl’s Guide 4: browning queen (b-q): A homosexual whose principal sexual interest is anal. Properly used with reference to passive partner, loosely used for active too (for which, rarely browning-king).
[US]Guild Dict. Homosexual Terms 5: b.q. (Browning Queen) (n.): A pederast, submissive or passive [...] browning queen (n.): A homosexual preferring pedication.
[US]Trimble 5000 Adult Sex Words and Phrases.
[US]B. Rodgers Queens’ Vernacular 146: passive partner [...] browning queen [sister].
[US]R.A. Wilson Playboy’s Book of Forbidden Words 50: The Browning family or the Browning sisters is exclusively homosexual slang for those devoted to this pastime [i.e. anal intercourse].