Season/Month
Although Beltane is becoming a popular time to hold Handfasting rites, May has traditionally been considered an unlucky month in which to wed, since that is the Gods' sacred marriage month. (It seems kind of like upstaging the Goddess on Her wedding day). This custom predates the Christianization of Pagan rites. It explains why June is such a popular month for weddings. I suggest you wait until the waxing moon in June. Samhain is also becoming a popular time for Handfasting Rites.
Day/Hour
The best day and time of the week to perform a Handfasting rite is either Monday or Friday at the first hour after sunrise or the first hour after sunset (but do cross reference this with the placement of the Moon and other astrological factors.) The worst days are Tuesday and Saturday, any time. If you can't make a Monday or Friday wedding, then at least try to perform the rite during the Magickal hour of Venus or the Moon. If you don't know how to figure out the hour of the Moon or the hour of Venus, Estelle Daniels does a great job of explaining magickal hours in her book "Astrologickal Magick" page 88 "Planetary Hours".
Astrology (Ignore this at your Peril!)
The best astrological time to perform the Handfasting rite is when the Moon is waxing to Full, well-disposed (that is: no hard angles to any signs, no angles to Mars or Saturn at all, and not Void-Of-Course) and in one of the Fixed signs. For more astrological hints, check out March and McEvers' book "The Only Way to Learn About Horary and Electional Astrology Volume VI" page 139.