You are correct Hurley, that it sounds stranger than was. I would surely get that incorrect in my writing and speech of this sentence - and I would expect (almost) no one to to notice.

There were no students on the playground sounds best. If you wanted to use the singular it would usually be to make a point that it looked deserted. There wasn't a student on the playground. Or: I got to the playground, but there wasn't a student in sight.

There was no student on the playground

The singular sounds kinda bizarre, usually plural. But a context like A: I saw a student left on the playground. B: What? That's impossible. There was no (even one single) student on the playground.