I heard that May-June is the best time to find housing. I've been checking pretty frequently, but yeah, finding a pet-friendly place is tough. I'm kind of freaking out that I won't be able to find somewhere by fall; apparently this year is actually worse than usual.
You might want to look at the Housing and UCSC housing pages on facebook, and the Community Rental Office. It's not that active, but r/SantaCruz might have some information. Maybe try Craigslist too?