Find and evaluate OA book publishers

Regarding selecting a publisher who supports Open Access books, the OAPEN website has a list of book publishers that have declared they comply with the open access requirements of a number of grant bodies, so this may be a useful place to start with identifying OA book publishers: https://www.oapen.org/researchers/13516596-funder-compliant-publishers

Directory of Open Access Books (DOAB) has around 400 publishers listed, and also provides the option to search for funder compliant publishers (use the Browse by links on the right of the page).

Search DOAB with keywords, and see results list of publishers on the right (black tab) which also shows how many books they have in DOAB relating to the search terms. Click publisher to see list of books by the publisher.

The DOAB sites notes that publishers who apply to have their books listed on the site are screened for their peer review process and licensing policy.

Predatory OA book publishing

As with journal publishers, you will need to assess book publishers and in so doing you should be able to identify predatory (i.e. deceptive and/or low quality) who may contact you or advertise for chapter contributions to a book. “Generally speaking a request for a chapter should come from a colleague - a scholar or scientist acting as editor for the publication. You should be able to check the credentials of this person or even better, already know this person. If this is not the case, then you should be cautious.” (DOAB site FAQ).
The DOAB site screens publishers for their peer review procedures and licencing policies. The Open Access Scholarly Publishing Association (OASPA) is a reputable site and has membership guidelines for OA book publishers. Check the membership list to see whether a publisher is a member.