As Steve says its usually the last weekend in July. Although it is one of the more recently established Road Races it is regarded as one of the better ones as the track is relatively short and the programme is quite extensive.
When heading over to the Thumper Rally at the end of July we meet three motorcyclists from Gloucestershire who had been to the Armoy Races and really enjoyed it. They had stayed in Ballycastle for a week and had visited other attractions in the area outside of the racing. I think camping is available in Armoy during the time leading up to the races. There's also quite a good vintage meeting on the Thursday evening as well.
Can't guarantee the weather though! Lol
Regards
Tony