Psychology labs often have full-time RAs as well, if you would be interested in doing psych research. If you're more interested in the biological side of things, many neuroscience-y psych labs have openings like this as well. It's hard to find out where these openings are, but you can start by emailing professors in labs/cities you'd be interested in working in to see if they have any openings. They might pass your resume on to people who do.
If you know what kind of psych you'd want to work in, you could check out the webpage for socieities for that kind of research. For example, I'm interested in working with infants/children, so I'd look at the International Society of Infant Studies and the Society for Research in Child Development for full-time RA jobs.
Good luck!