The first sentence focus on the amount of tables. You could use it when someone expects there to be tables, but realizes that there aren't any. The second just states that there are no tables, but seems more like it is being emphasized that it's "tables" that are not in the room as opposed to something else. You might use it when you want to say, "There are lots of chairs, but no tables." But really, this is a very small difference, and you could use the sentences interchangeably, in my opinion.

Sarah's comments about the emphasis in meaning are right, but neither of these sentences is correct in English. We would say: There aren't any tables in the room. There are no tables in the room.