Jews For Jesus. It sounds like a joke, doesn't it? Jewish comedian Jackie Mason said there's no such thing as a Jewish Christian: "You're either a table or a chair." But they are a real organization, and, like most religions, they have music.
A group with the somewhat unwieldy name of The Liberated Wailing Wall (now, how are they gonna fit THAT onto t-shirts?) have been singing the praises of Y'shua ("Jesus" in Hebrew) since the early '70s, and much of their music is available for free (scroll halfway down this page.) Some of it still retains that early-'70s "I'd Like To Teach The World To Sing" feel to their vocal harmonies, but they command a wide range of styles, most successfully when they kick out the klezmer jams.
Klezmer is a frantic Eastern European polka-like dance with a punk-rock tempo. It's lots of fun, especially when it's a showtune-like bar mitzvah song about a young Jewish boy accepting Jesus. Kinda weird that's it's sung by a woman, but, then again, so is the entire concept of Jewish Christians.
The Liberated Wailing Wall: "Today I Am a Man"