I found sheeny used as a group definition in 1797:
SHEEN, fhe'n. 7 a. Bright, glit- SHEENY, (he'n-y. 3 tering, fhowy. SHEEP, fce'p. f. The animal that bears wool ; a foolith filly fellow.- A complete dictionary of the English language, both with regard to sound and meaning :... but not a antisemitic reference; notably, the negative connotation is that 'sheepbiter' was a thief, and 'sheepbite' was petty theft.
By 1891, The American slang dictionary, by James Maitland defined
Sheeny, a Jew. The origin of the word is much disputed.
Published in Wisps of wit and wisdom, 1892:
463.—How did the term," Sheeny," originate? As a result of the kindness shown to them, by the na- tions among whom they lived during the Middle Ages, the Jews, out of love for their neighbors, came to use as a bene- diction, salutation, valediction or malediction, the fervent wish, "Misah Meshina!" (" Mayst thou die one of the five judicial deaths !") Thus, a German baron pulling out the rabbi's beard was prayed for by the whole congregation that he might take a Misah Meshina. The use of this curse became common to the extent that it was used on the slight- est provocation, and the English, catching the terminal sound from the same class of people, constantly used it, or its corruption, "Sheeny," to designate them in slang phrase.