How could we detect planets orbiting black holes?

Gravitational microlensing is a way of finding planets that does not care how luminous or otherwise the hosts of the exoplanets are.

The way it would work is that you stare at a dense background field of stars; then when a foreground black hole passes in front of a background star, the light from the star is magnified by gravitational lensing. Typically, the lensing event takes a few weeks for the magnification to develop and subside.

If the black hole has a planet, it may be possible to "see" its graviational potential, which will manifest itself as an asymmetry in the lens light curve or possibly even a little extra spike in the light curve lasting a few hours.

This technique is well established and is already used to detect planets around unseen objects. It is more sensitive than the transit and Doppler methods to planets orbiting a fair distance from their parent star.

The difficulty here is not finding planets around a black hole, it is proving that the planets you found were actually orbiting a stellar sized black hole. The microlensing event would only be seen once and the black hole system would likely be invisible. There is a possibility I suppose that it may undergo some sort of accretion activity after having been found by lensing, and this accretion might then be picked up by telescopes trying to identify the lensing source. I guess a good place to start would be events where a stellar-mass lens is inferred, but no star can be seen after sufficient time has elapsed that the lens and source star ought to be resolved.