These are publishers who promote their plays through national conferences and events and represent the top playwrights. Visit their booths at conferences. Send for their catalogues. Explore their Web sites. Don't try to publish your play too soon.
Publishers often require several productions before they'll consider a script for publication.
If you play is good, it probably could be better. During this time also try to interest publishers by letting them know about the play, try to get them interested in following the growth of the play through its different productions. Don't send a publisher your first draft. Even if they ask for it. Most playwrights writing for young audiences do not have agents.