I wasn't aware, and this video, from historian Miranda Kaufman, is very interesting. Some of what I learned here may be included in my next book, if the right character finds me.
I've seen black characters in some recent historical productions (The Spanish Princess comes to mind), but I think these have been taken a little far - while Katherine of Aragon may well have brought black servants with her from Spain, it's very unlikely that one would have been her lady-in-waiting. That wouldn't have been a race issue, but the fact that ladies-in-waiting were generally high-born young women, maneuvered into those positions by their families to get them close to power, powerful men, and advantageous marriages.
On the other hand, as noted in this video, Henry VII (big Henry's dad) did have a black trumpeter named John Blanke, so while there weren't likely black courtiers, there were black people at court.
This is one of the things I love about history - you keep finding out new and interesting bits that you hadn't expected, and they keep leading you deeper and deeper.