What possible word that begins with D and ends with Y is used in racial context?
Darky is the word you are looking for.
OED:
darky | darkey, n. ... 3. Also darkie. A black person, esp. from the southern U.S. Also attrib. colloq. (offensive).
1840 R. H. Dana Two Years before Mast xxxiii. 129 The darkey tried to butt him.
1848 J. R. Lowell Biglow Papers 1st Ser. ii. 24 I'd an idee thet they were built arter the darkie fashion all.
1883 Cent. Mag. 27 132 The manners of a corn-field darky.