"morbid fear of clowns," by 2001 (said in Web sites to date from 1990s or even 1980s), a popular term, not from psychology, possibly facetious, though the phenomenon is real enough; said to be built from Greek kolon "limb," with some supposed sense of "stilt-walker," hence "clown" + -phobia.
Ancient Greek words for "clown" were sklêro-paiktês, from paizein "to play (like a child);" or deikeliktas. Greek also had geloiastes "a jester, buffoon" (from gelao "to laugh, be merry"); there was a khleuastes "jester," but it had more of a sense of "scoffer, mocker," from khleuazo "treat with insolence." Other classical words used for theatrical clowns were related to "rustic," "peasant" (compare Latin fossor "clown," literally "laborer, digger," related to fossil).
Coulrophobia looks suspiciously like the sort of thing idle pseudo-intellectuals invent on the internet and which every smarty-pants takes up thereafter; perhaps it is a mangling of Modern Greek klooun "clown," which is the English word borrowed into Greek.