Heya, well I bounced the idea across the sca archery mailing list and they came up with some interesting ideas..
St Sebastien is the christian patron saint of archers and he has a day on 20th of January.
Not sure if it qualifies as a diety but certainly mythological - Chiron, the Centaur who was said to had become the constellation Sagittarius, the Archer. But, like most pre medieval figures doesn't have an identifiable date association.
as well, Diana (or Artemis), Goddess of the Hunt, always depicted with bow and arrows.
She was worshipped at a festival on August 13.
Hurn the hunter, Apollo and of course Cupid were mentioned as possible ideas as well.
Throughout history man kind has venerated and celebrated the bow and the figures who used them. maybe one of these figures can help us find a day to celebrate this on?
Live long, Drop dead.