Need Two Referees - I only worked with one referee extensively for research

I’m having a bit of issue with providing references for psychology postgraduate application.

One of my top-choice universities specifies that they need two referees who can comment on my research experiences. The problem is I only have worked extensively with one amazing professor (my home had a very small research sector in psychology) and have worked only a bit with another who hardly publishes at all. I know the former would be quite willing to provide a good reference, but I am not so sure with the latter as we haven’t worked together much. There’s also the “publish or perish” mentality, so I’m worried it will reflect badly on my overall application.

I do have many potential referees who have either taught me or I have worked for and I am pretty certain they would say very positive things. However, they don’t have much contact with me in the research field. So my question is, what should I do? Do I go with the two research referees as the university stated or maybe use my other (non-research) referees for the second references?