They'll have to be HHHL - Half Height Half Length - or smaller. I'm not sure any are other than the bottom of the ranges - a quick search found a GeForce 710 in that size, but that's fairly puny. I did also find a K620 in low profile, but I suspect it'll be too long; try looking at your favourite supplier for "low profile" to start with, the best I can see is a single slot K1200 from Leadtek, but again length could be a problem.
TBH I would not try this. Space/ cooling wise you are going to use extremely small GPUs. I do have a bunch of the GRID M40's (Tesla M10's with half the RAM) in blade servers. They are super low power so they work well (2 slots gives 8x GPUs). When I get a chance I want to have a Docker ML cluster using them.