About the only thing I do different for black wheels is I will always finish up with a spray wax while drying them to make sure there are no water spots left behind. I'll usually check them well after I clean them to make sure I haven't missed anything. Black wheel show dirt and water spots well.
Also, maybe use more gentle brushes or Wheel Woolies. Black likes to show scratches well too.
I they are flat black, maybe some others can give advice on what to use.
For easier upkeep, apply a good wax, sealant, or dedicated wheel coating and clean lightly often.