Pheidole megacephala can be listed in March and July, maybe September if you want to list that month. While their main biggest flights/budding out isn't till August, they actually officially start in July. And technically, depending on the climate, they can bud out year round sporadically. Here in California I've actually seen them bud out really early in the year, which earliest I've seen them bud out is in March. After March (taking my observations of last year and the year before), they seem to not bud out nearly as much till again in July. And I'm not talking about just general colony growth/expansion, but actual mating "flights" where they bud out to new areas with queens.
So pretty much 3 months of budding out (March, July and August), in the months I've seen them consistently bud out with new queens. They go into early September as well, but after the 1st week of September they go semi-inactive. Its really only the first week of September they bud out still, so not sure if you want to list that month for them.