There is no bad time to come. There is only a wrong coast for the month you have chosen.
Almost every article about when to visit Sri Lanka gives you a single answer, usually December to March. That answer is not wrong so much as it is half the island. Sri Lanka sits in the path of two separate monsoons that arrive at opposite ends of the year and hit opposite sides of the country, which means that on any given day of any given month, somewhere here is in its dry season.
The two systems
The southwest monsoon, or Yala, runs roughly May to September and soaks the west and south coasts along with the hill country. The northeast monsoon, Maha, runs roughly October to January and takes the east and north. Between them are two inter-monsoon periods that can produce afternoon thunderstorms anywhere, which pass quickly and are rarely a reason to change plans.
December to March
The south and west are at their best: Galle, Mirissa, Tangalle, and the whale migration off the southern coast. The Cultural Triangle is dry and warm. This is also the busiest and most expensive window, and the popular beaches genuinely fill up. If you are coming now, book earlier than feels necessary.
May to September
The east comes into its own. Trincomalee, Arugam Bay and Pasikuda are dry and calm while the south is being rained on, and the surf on the east coast is at its most reliable. Yala is dry and the animals concentrate around the remaining water, which is the single best condition for seeing leopards. Fewer visitors, lower prices, better wildlife.
What we actually do
We start from your dates rather than from a season. If you can only travel in July and you had pictured the south coast, we will say so plainly and move the trip east, which is usually a better holiday than the one you asked for. The island is small enough that this is a change of coast, not a change of country.