Origin of "moke," used in the mildly derogatory term "you lil' moke"

'Moke' in U.S. slang

As a U.S. slang term, moke has a very problematic history. Though its earliest slang meaning (going back at least to 1839), was "donkey or mule," it was also used for decades as a disparaging term for "a black or dark-skinned person" (starting not later than 1847) and "a foolish or inconsequential fellow" (starting not later than 1855).

J.E. Lighter, Random House Historical Dictionary of American Slang (1997) identifies three basic meanings of the term in connection with living creatures:

moke n. {orig[in] unk[nown]} 1.a. a donkey or mule. Rare in U.S. b. a horse. [Citations range from 1839 to 1960.] ...

2.a. a black person.—usu. used contemptuously.—usu. considered offensive. ... b. a dark-skinned person of any race.—usu. used contemptuously.—usu. considered offensive. [Citations range from 1847 to 1967.] ...

3. a foolish or inconsequential fellow. Cf. MOOK. [Citations range from 1855 to 1915] ...

So historically in U.S. usage, a moke could refer to a beast of burden; a black or dark-skinned person; or a fool or lightweight.

George Matsell, Vocabulum; or The Rogue's Dictionary (1859) is one of the earliest glossaries to list moke:

MOKE: A negro.

James Maitland, The American Slang Dictionary (1891) indicates that the first two meanings cited by Lighter were used in different parts of the world:

Moke, in England a donkey; in the United States a negro.

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Theories of the term's origin

As for the source of the word (which Lighter says is unknown), different theories have appeared over the years. Maximilian Schele de Vere, Americanisms: The English of the New World (1872) has this for moke:

Moke, possibly a remnant of the obsolete moky, which is related to "murky," is used in New York to designate an old fogy or any old person, disrespectfully spoken to. A hackdriver is thus represented to reply to a stranger who had upbraided him for his violent language, "See here, my lively moke, said he, you sling on too much style." (Galveston [Texas] News, May 4, 1871.) In the Northwest the term is generally applied to negroes, with whom the original "murky" may be associated in some minds. "The young mokes, who had often denounced Mr. Ham for having incurred the displeasure of his aged sire, in consequence of which their heads were covered with tufts of hair." (Dubuque [Iowa] Herald, 1871.)

"Billy Bilger" [Andrew Pendleton], The Silly Syclopedia: Containing "daffynishuns" of the Words of the Slang Language Spoken by the Midshipmen of the U.S. Naval Academy (1908) has this:

MOKES—(From the Spanish Mozo meaning servant.) The sons Ham with waiter's billets. Blackheads on the face of the earth.

An illustration of "mess hall moke" in the same book clarifies that Naval Academy midshipmen used the term to refer to (African American) food servers and table bussers in the mess hall.

Harold Wentworth & Stuart Flexner, Dictionary of American English, first edition (1960) has this:

moke n. 1 {derog.} A Negro, esp. a Negro minstrel. 1856: D[ictionary of] A[merican] E[nglish]. 1899: "Smoky Mokes," title of a pop. song. Obs. From "mocha." 2 {derog.} A Filipino. Some c1930 USN[avy] use. 3 An easy-going fellow; one who habitually asks favors; a bore. Some c1900 use. 4 A horse, esp. an inferior race horse; a plug. Not common in U.S. but fairly common in Australia. adj. Dark; black; Negroid. Not common.

To sum up, the suggested source words are murky (suggested in 1872), mozo (suggested in 1908), and mocha (suggested in 1960).

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The Romani connection

John Hotten, The Slang Dictionary: Or, The Vulgar Words, Street Phrases, and "Fast" Expressions of High and Low Society (1864) alludes to an alternative etymological explanation that may be of special interest to the poster:

MOKE, a donkey.—Gipsy.

The 1874 edition of Hotten, The Slang Dictionary: Etymological, Historical, and Anecdotal, expands this entry considerably:

Moke, a donkey.—Gipsy, but now general to all the lower orders. A "coster" and his " moke" are almost inseparable terms. Probably derived originally from the Arabic al mocreve, a carrier.

Hotten's dictionary was published in London, and he is clearly concerned with the British English meaning of the slang term moke. A letter by William Cumming Wilde, published in American Notes and Queries (December 22, 1888) follows up on the etymological question:

MOKE, a negro (Matsell's "Vocabulum, or Rogues' Lexicon," New York, 1859). Moke, a donkey, Gipsy, but now general to all the lower orders ("The Slang Dictionary," London, 1873). Meila moila, and not moke, is the English Gipsy for donkey. In Stratman ("Dictionay of Old English," 1873) we find: Moke; Swed. mocka, moke, etc. Moke (môk-mok?), moke, tined; but neither of these would seem to be the moke that appears above. The English Gipsy and Moker, to foul, dirty—Smart and Crofton, "Dialect of the English Gipsies," 1875—may seem to be the source from whence we get moke, but we object to this; moker is not to be seen in any other Gipsy, except the English; nothing in any way like it can be found in the Gipsy dialects of Norway, Germany or Spain.

In "Paspati Études sur les Tchinghaianés ou Bohemiens de l'empire Ottoman," it is true, we have mokára peindre, tacher, graisser, but this would hardly seem to suggest moke. In our Old English, we find mokey defined cloudy, and so may be allowed to suppose that moker is quite as likely to be English as Gipsy. Certain it is moke existed in our English literature at least one hundred and fifty years before the first Gipsy appeared int he British Isles. "Crist," says Wycliffe, "gave his life for hise breper, & so rewled his shepe; pei wolen not gyne her moke to help here nedy brepern, but leten here shep perishen." ...

Moke, in Wycliffe's Treatise, evidently expresses servant, menial, even if it may be suggestive of something that is filthy or foul. The reverend doctor [James Todd, D.D. Dublin]'s troubles [in identifying the meaning of moke in Wycliffe] may, at least, teach us a lesson; thief talk is not without its uses, and it is certainly not gibberish, as some suppose.

These references suggest sources of moke in Arabic al mocreve (in 1874), in "English Gipsy" mokar (in 1875), in Swedish mocka (in 1877), and in Old English mokey (in 1888).

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Conclusions

Whatever the original source of moke in the British English sense of "donkey" may have been, the fact that it was identified with "English Gipsy" slang by 1864 and that it appears to have been used as a term of endearment (or perhaps of affectionate exasperation) by a Romani grandmother more than a hundred years later is fascinating to me. To judge from the OP's anecdotal evidence, the Romani English sense of moke does not appear to have been tainted by the derogatory U.S. English sense of moke as "dark-skinned person."

"See here, my lively moke, said he, you sling on too much style." (Galveston [Texas] News, May 4, 1871.

This quote is a reference to a blackface song-and-dance routine popularized on the American variety stage by Johnny Thompson and later by William J. Ashcroft and other minstrel performers. The lively (or "musical") moke danced, sang and played various instruments. Ashcroft later did much the same routine in Irish character with "MacNamara's Band."