Can you eat watermelon on a low carbohydrate diet?

Yes, there's is absolutely nothing wrong with it. Unless the diet says otherwise.

The are a lot of low carbohydrate diets out there. Different recommendations in different diets. I've added a link (scroll down a bit) which shows the carbohydrate amount in watermelons. There you can check if it's acceptable in your low carbohydrate diet or not.