I am currently in the same boat, but I have found it easy to find paid research positions that schools are taking applications for. Most, however, are not really that close to where I live. But schools such as Indiana University, which is near me, have school of medicine departments that perform a lot of research, and are constantly hiring assistants and technicians to work in clinical and non-clinical labs. I have had several in-person interviews for clinical research positions, although I have been unsuccessful thus far.
Look at the employment sites for universities near you, or where you would like to work. Some may allow you to filter for "Research" positions, or you can enter "research" into a search field and look that way. I also look for jobs at Indeed.com (or other job search engines) and Higheredjobs.com. I usually just enter "Psychology Research" into the search area and find jobs that way. You can also get creative and look for private institutes via google that have employment opportunities in research. Paid research positions for post-bachelor grads DO exist. There are just not that many in some areas or at some universities.
Just a heads up though, out of the god knows how many applications I have submitted across the country, I have only heard from 3 schools regarding positions that I applied for outside of the state I live in, while I have heard back from IU about 4 of the 5 positions I met qualifications for. It appears that most schools really only look at qualified applicants in their area.