(Falconer and Falcon(e)ry are actually individual costumes from completely different sources, though close together in time, but they'd also make a workable pair of themed costumes for a couple, despite their disparate historical styles. It seems a bit unfair that the lady gets a hawk, presumably stuffed, and the gentleman does not!)
For the gentlemen, a Falconer:
FALCONER
Short tunic of brown velvet trimmed with a plastron of gold cloth and bound with gold braid, fastened round the waist with a leather belt. Loose knickerbockers, gartered at the knee, and tied with a ribbon bow. White stockings with calf-pieces of velvet trimmed with gold braid. Leather shoes. Lace neck-frill. Soft, round hat of velvet, trimmed with eagle feathers.
Source:
Masquerade and Carnival. New York: The Butterick Publishing Company, 1892.
For the ladies, Falconery:
FALCONERY
Short skirt of dark cloth, red, blue, or brown; green velvet skirt caught up on one side; long basqued jacket of the same; gauntlet gloves with hawk on the hand. Cavalier hat with dropping feathers; high boots.
Source:
Holt, Ardern. Fancy Dresses Described, 5th Edition. London: Debenham & Freebody, 1887.
Nine years later the description is virtually the same, though the velvet overskirt is lost and the spelling is more conventional:
FALCONRY
Short skirt of dark cloth, red or brown; long basqued jacket of green velvet; gauntlet gloves; a hawk on the hand. Cavalier hat with dropping feathers; high boots.
Source:
Holt, Ardern. Fancy Dresses Described, Sixth Edition. London: Debenham & Freebody, 1896.
The 1896 edition of Holt may be found online at the University of Wisconsin Digital Collections.