It is not just an RF chamber. All tests require not only the right equipment but also the right setup (shielding, non conductive tables, etc, etc). If you want to make accurate measurements without a huge investment then there is no alternative than to rent a lab for a couple of hours.
I've never seen anyone rent out an RF chamber without the whole package or equipment and personnel needed for the standard suites of tests..
I would suppose, if you went to a testing lab and requested a custom quote for chamber time only, no support, you might get a good deal.

Or laughed off.

Low frequency (conducted) and transient stuff is easy enough to test with a ground plane. You will easily see if there are nearby sources of interference (radio stations, maybe some particularly obnoxious power supplies?), which you'll have to subtract from your test.
Radiated can be done with an open-air test site, but you have to subtract even more ambient sources (potentially). Or carefully select a site, and antenna direction (assuming you have sufficiently directional antennas), to get it quiet enough to actually perform the test. And you need a good enough antenna / selection of antennas (I usually see conical dipole for 30-200MHz, log periodic for 200-1000MHz). This definitely makes it more challenging to do radiated emissions outside of a test lab. (And, not having a way to calibrate, say, 3 V/m emitted field intensity, and avoiding beaming that at just any radio user that happens to be nearby, is even more tricky!)
Tim