Recommenders that are professors but not co-authors I applied to a junior faculty position in a certain university. They asked me to provide a list of recommenders with the following requirements:


Each recommender should be a professor.
No recommender can be someone with whom I wrote a paper.


The second requirement rules out not only my Ph.D. advisors, but also most professors who know me as a researcher. I thought of several ideas for recommenders that meet both these requirements:


Professors who meet me regularly at department seminars. They can (hopefully) testify that I can ask good questions. But this is only a small part of being a good researcher.
Professors whose courses I took as a graduate student. They can testify that I can learn well. But again, this is only a small part of being a good researcher.
Professors for whom I did some technical work, e.g. computer programming (for research purposes); same comment as above.
Editors of journals for whom I reviewed a paper. They can (hopefully) testify that I can write good reviews; same comment as above.
Editors of journals in which I published papers. They can (hopefully) testify that my papers are good. But, the fact that they published my papers already shows that they think it is good.
Professors for whom I worked as a TA. They can (hopefully) testify that I know to teach. But for this, it may be much more relevant to bring recommendations from students (which I have).


What other options do I have?
People who cite your papers

A particular audience that is suitable for this are people who cite your papers. It is quite likely that the committee wants to see what impact (if any) your research has on your field, so they would want opinions from people outside your team that have read your research and find it useful. One way to find such people is to look at citations to your papers - they (obviously) have read your research, consider it valuable, and you should be able to find their contact information from their papers.