County Antrim is wet year-round — this is the north coast of Ireland — but summers (June to August) bring the longest days and the most reliably passable weather for outdoor activities like walking Slemish or exploring the Glens. The school summer holidays (mid-July to August) are the busiest period; the Giant's Causeway and Carrick-a-Rede can be crowded then.
Spring and early autumn are often the best times to visit: fewer crowds, the landscape is green, and the light on the Antrim coast can be exceptional. March is worth noting for one specific reason: Slemish Mountain draws very large numbers of pilgrims on St Patrick's Day (17 March), which is either an atmospheric experience or a reason to visit the mountain on any other day.
Winter is quiet and can be grey for extended periods, but accommodation is cheaper and the coast has a stark quality that some find more compelling than the summer version. The Galgorm spa is a reasonable way to spend a wet winter day regardless of season.