OED:
Moke
Summary: Of unknown origin. Compare English regional (Hampshire, Devon) mokus donkey.
Notes: In the 16th cent. proverbial phrase ‘Mocke (or Mok) hath lost her shoe’ (Skelton Why come ye nat to Courte, 83, Goodly Garlande of Laurell 1396) it is possible that Mocke is a name for a donkey or a mare (compare Skelton's use of mockish adj. 2), although connection with modern moke is unlikely.
Senses 2 and 3 may be etymologically distinct.
1.a. A donkey.
1839 Moak, a donkey. H. Brandon, Dictionary Flash or Cant Language in W. A. Miles, Poverty, Mendicity & Crime 164
1.b.In extended use: a person who is stupid, awkward, or incompetent; a dolt, a fool; = donkey n. 2a.
1855 He has an irreconcilable grudge against a poor moke of a fellow called Archer Gurney. D. G. Rossetti, Letter 25 November (1965) vol. I. 282
2. c1847– U.S. derogatory (offensive). A black person. Also (in extended use): a dark-skinned person of any race. Now rare.
3.1890† Theatre slang. A performer who plays several different instruments. Obsolete. rare.
It's worth noting that the British English use of moke (which is very rare) has absolutely no racial connotations - in fact there was a popular version of the Mini car that was marketed under the name of "Mini Moke".