fruit of the blackthorn, Old English slah (plural slan), from Proto-Germanic *slaikhwon (cf. Middle Dutch sleeu, Dutch slee, Old High German sleha, German Schlehe), from PIE *sleie- "blue, bluish, blue-black" (see livid).
The vowel has been influenced by that in the old plural form, which according to OED persisted into the 17c. Scottish slae preserves the older vowel. Sloe-eyed is attested from 1804; sloe gin first recorded 1878.