Douglas Harper's Etymology Dictionary
sheeney
"a Jew," 1816, of unknown origin; perhaps related to Russian zhid, Polish żyd, Czech zid "a Jew." Now a vulgar term of abuse, but used before c.1870 by Jews and Gentiles without intent of insult.
Usage examples of "sheeney".
According to the stories, and there are hundreds told about him, he was the smoothest Sheeney that ever swore by Moses.