A little preliminary information from the OR, series 3, volume 3 (general correspondence of US authorities for 1863):
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Excellent discussion of conscription! In early October 1863 the Lincoln administration, over the strong objection of some border state Unionists, instituted a remarkable and little-known policy of compulsory emancipation of enslaved men, with compensation to their previous owners, in most of the border states, and of their enrollment in the army, effectively extending the draft to slaves and providing the essential foundation for the extension of full citizenship. The policy was kept secret for a time and not applied in Kentucky at first because it was so potentially explosive.
Prof. Knupfer's has helpfully clarified his original intervention. Prompted by my discussion in "Freedom National" of the way slaves were recruited into the Union army in the southern states, Prof. Knupfer asked whether in fact any blacks were ever drafted. I replied by pointing out that recruitment in the slave states was organized very differently than the way it was organized in the northern states. I was arguing the very point that Prof. Knupfer now makes: that conscription and impressment were hard to distinguish in the South, and that it was controversial for just that reason.
I really appreciate the contributions so far and will dig into the references that are coming in.
I'm grateful to Prof. Oakes for his clarification about the discussion of "drafting" blacks into the Union Army. But I fear he misunderstands me, so I'll try to be a little clearer, if possible.
I have done a little research on this in Kansas. To my knowledge, no, there were no black draftees in 1863.
Though, in Kansas and Missouri, some who served in USCI regiments had been impressed into service and many in the 1st and 2nd Kansas Colored had previously served in Lane's Brigade. James Lane recruited black regiments under the Militia Act of 1862 (despite protests from higher ups that this was illegal). They were not formally mustered into service until 1863. This was not a draft, however.