JK Rowling has answered this question herself in a Pottermore article on the Dursleys. The most interesting one is Petunia, whose name apparently comes from a half-remembered cartoon JKR saw as a child featuring an uncaring woman called Petunia. Quoting from the article itself (emphasis mine):
Vernon and Petunia were so-called from their creation, and never went through a number of trial names, as so many other characters did. ‘Vernon’ is simply a name I never much cared for. ‘Petunia’ is the name that I always gave unpleasant female characters in games of make believe I played with my sister, Di, when we were very young. Where I got it, I was never sure, until recently a friend of mine played me a series of public information films that were shown on television when we were young (he collects such things and puts them on his laptop to enjoy at leisure). One of them was an animation in which a married couple sat on a cliff enjoying a picnic and watching a man drowning in the sea below (the thrust of the film was, don’t wave back - call the lifeguard). The husband called his wife Petunia, and I suddenly wondered whether that wasn’t where I had got this most unlikely name, because I have never met anybody called Petunia, or, to my knowledge, read about them. The subconscious is a very odd thing. The cartoon Petunia was a fat, cheery character, so all I seem to have taken is her name.
The surname ‘Dursley’ was taken from the eponymous town in Gloucestershire, which is not very far from where I was born. I have never visited Dursley, and I expect that it is full of charming people. It was the sound of the word that appealed, rather than any association with the place.