Many fish now have long finned varieties, I'd stay away from them all: BNs, rams & some corys all have that mutation. I prefer normal finned fish anyway. If you have hiding spots &/or lots of plants they may work especially with a few more tetras. I think a cory group or a bn should be Dad's next move. Then see how the tetras behave. The foot print on a 37g is only 30 x 12 inches, so corys & a BN would pretty much fill the floor space.
If his heart is set on cichlids eventually, you might skip 1 or the other species since they're all virtually bottom dwellers too. If he had a pair small cichlids (rams, kribs, or apistos) he'd get the interesting breeding behavior & the tetras would take care of (almost?) all of the fry.
the best option IMO.