While I'm not sure what running time you're looking for, a few thoughts on plays for two men:
The Zoo Story by Edward Albee, which others have already recommended. Probably my favorite one-act of all time.
Lonely Planet by Steven Dietz, an absolutely gorgeous play about AIDS, though it never actually mentions it by name.
The Mystery of Irma Vep, Charles Ludlam's hilarious satire, and a whole lot of costuming fun.
Of course, these are all challenging pieces for young actors, as all were intended for adult performers. But that's another discussion. Happy hunting.
Cheers,
Jonathan
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Jonathan Dorf
Playwright/ Co-founder of YouthPLAYS/ Co-chair of The Alliance Of Los Angeles Playwrights
Los Angeles CA