In prose, should a transliterated song title appear in italics or quotation marks?

In prose, style a transliterated title the same way you would style the title in English.

In the following example, the transliterated title A fidler afn dakh is styled in italics because, as noted in the MLA Handbook, titles of independent works, such as musicals, are styled in italics (25–26). The transliterated title “Traditsye” is styled in quotation marks because, as the handbook explains, song titles are generally styled in quotation marks (28): 

In a recent Yiddish version of Fiddler on the Roof (A fidler afn dakh), the cast sings “Traditsye,” an adaptation of the English-language song “Tradition.”

Work Cited

MLA Handbook. 8th ed., Modern Language Association of America, 2016.