To start with, a (non rotating) black hole and a star of the same mass creates the same gravitational potential when you are far away enough. Since we observe planets at $0.05\mathrm{AU}$ around stars of about the same mass as the sun, I think you can expect planets in this region around a similar mass black hole, according to stability criterion. Moreover, the smallest black holes you can physically create have masses of about $3-4 M_\odot$.
There are multiple issues here though. First is how do you physically bring the planet that close to the black hole? I see two possibilities. Either the planet formed directly in the accretion disk of the black hole, and staid there, or the planet formed further away (say around the binary star system) and was captured by the black hole. If you assume that at $0.05\mathrm{AU}$, the accretion disk of the black hole is not that different than the accretion disk around a protostar at early ages, then you can maybe create a planet there (I can think of a few scenario that would prevent it, but it would require a more important study). If the planet formed further away in the disk or in the binary system, it is possible to make it migrate inward. 788
This is actually called ex-situ formation in planetary systems.
If you imagine that the planet is tidally locked (you can try fiddling around with the formula $t_{\text{lock}} \approx \frac{\omega a^6 I Q}{3 G m_p^2 k_2 R^5}$ from wikipedia that gives the timescale for the planet to become tidally locked to get an estimate of how long it would take) and that there is no accretion disk anymore, I guess you could manage to make the system stable.
The final question is then to get the whole system stable on a large. Even though it may extremely unlikely, I think there has to be some stable orbits in the system using 3 body resonance, but this is not my field of expertise. having one or two stars is not making a huge difference, between the flux received from them and the gravitational pull are both in $1/r^2$, so that two stars at 1.4AU give the same flux and the same mean gravitational pull than one star at 1AU. The only difference is in the stability of the system.
To conclude, I guess that the system is very unlikely to exist. Yet if you manage to find a planet there, you'd require to have life:
1. the accretion disk of the black hole has to be cleared
2. the planet should be tidally locked to the black hole to be protected from the radiations
3. the planet should be trapped in a very unlikely stable orbit so that it doesn't travel around in the system AND it has time to get tidally locked to the black hole 788