The problem, it seems, is the extreme dynamic range and ultra explosive transients produced by the instrument.  Often recording engineers will simply ask you to play at half volume to solve these problems and get a decent recording.  Micing a djembe for a PA is even worse in that a djembe is a DANCING drum which is typically worn and played standing! Sure maybe you could clip an SM57 on the drum rim, but here is a far better answer. One that not only easily allows a wireless system to be hooked up, but also will give you killer tone all your bass, tone and slap sounds.

        The Answer as shown on the left is to simple attach a Pick-up the World Model  #20  Piezo film pickup to your drumhead as shown on the left! This single pickup works equally well on bass, tone and slap sounds. No overload!  Clear as a bell! No bulky mics! 
          But to get nice bass out of these devices you MUST have a very high impedance preamp.  1 megohm or more is needed. The usual 100k guitar amp input will roll off your bass!
Happily, really nice EMG preamps are available from Pick-up-the-World.

PICK-UP-THE-WORLD is a Dr. BenGenius patron and sponsor. They have supplied all the pickups for these experiments.  Dr. BenGenius is VERY enthusiastice about their products (and not just because of freebies, but rather because of the SOUND!)  Djembes are simple to pick up, but congas are much more of a problem.  That is why the Electric Conga project is still "under Construction"
Watch this website for progress on this killer project.  You are gonna LOVE it when it's done!