1803, from French contre-danse, altered from English country dance by folk etymology from French contra "against," suggested by the arrangement of the partners in the dance. The dances and the name were taken up in France c. 1720s and from there passed to Spain and Italy (Spanish, Italian contra danza) then back to English.
Examples from the Web for contra dance
Will you do me the honor, lovely coryphe, to accept my hand for this contra-dance?Monsieur Cherami
Charles Paul de Kock
Pretty soon, music—organ—sometimes grand and solemn, but generally fast and lively enough for a contra-dance.Doesticks, What He Says
Q. K. Philander Doesticks
They now passed in the contra-dance; Eve's hand was not slow in taking Louise's; the two girls shivered at once.
Contra-dance is better than country-dance, the latter word being a corruption; but it has become admissible from long use.Every-Day Errors of Speech
L. P. Meredith
The figures were compounded of the contra-dance and reel, with some remarkable touches of the Mandingo balance.Journal of an African Cruiser