Ah, thanks, I should have thought of that. Here's the data I was looking for with the first few primary states. As you can see, the exit poll data is very incomplete; more sources are needed.
---(February)---
IA: 93% White, 4% Black, 3% Other
NH: [not recorded]
NV: [not recorded]
SC: 43% White, 55% Black
---(Super Tuesday)---
AL: [not recorded]
AR: [not recorded]
CO: [not recorded]
GA: 42% White, 52% Black
MA: 85% White, 6% Black, 5% Latino
MN: [not recorded]
NC: 63% White, 33% Black
OK: [not recorded]
TN: [not recorded]
TX: 49% White, 19% Black, 30% Latino
VA: 62% White, 30% Black
VT: [not recorded]