Discovering poetry book publishers can be a challenging task, but there are a few ways to go about it:
Research: Look up poetry publishers online and read about their mission, the types of poetry they publish and their submission guidelines. This will help you get a sense of which publishers might be a good fit for your work.
Check out literary journals and magazines: Many literary journals and magazines publish poetry, and many also have a book publishing arm. Submitting your work to these journals and magazines can help you get your foot in the door with a publisher.
Attend poetry readings and events: Attending poetry readings and events is a great way to discover new poets and publishers. You can also network with other poets and potentially learn about publishers through word of mouth.
Join writing organizations: Joining writing organizations such as Poets & Writers, The Academy of American Poets, and The Writer's Union can provide access to resources like literary magazines, contest listings, and information on small presses and literary agents.
Take a look at the books already in your local bookstore. Often the publisher information is on the cover.
Research literary agents who represent poetry and check out their client list to see which publishers they work with.
Ultimately, the key to discovering poetry book publishers is to be proactive and do your research. It may take some time and effort, but it will be worth it in the end to find the right publisher for your work.