Perhaps this will save you a bit of that frustration. The photo above is of my friend Marianne's dining room. She recently replaced her dining set with a round table and upholstered chairs in a pretty plaid to complement the yellow and blue toile wallpaper.
She searched all over for a round rug that would fit into the French country decor... and would have the same blue from the chairs and wallpaper... and would be the right size as well as shape. She thought she finally found one online, but it was wrong. That meant paying for shipping - twice.
Finally: The answer! She went to a local carpet store and discovered you can have a carpet cut and bound into any shape you want. Most of us know you can get a rectangle or square cut, but there are all sorts of possibilities. Marianne found several options that would have worked just fine, picked the best one and had it cut into the size circle she needed.
Here's one more trick you can steal from Marianne: While waiting to find the perfect round table for her dining room, she had someone cut a plywood circle and put it on top of her old, oval dining table (with a table cloth).
The carpenter put a little lip on the plywood in a few spots so it wouldn't slip. And you'd want to put a table pad underneath the plywood so you don't scratch the table.
Clever, clever girl, Marianne is. Think I'll hang around with her for another 30 years to see what else she comes up with ...
Update: I've added another photo of the room so you can see the wallpaper as well. I also got a few questions about the cost. Of course, the price of a custom job like this would depend on a few factors, including where you shop, how expensive a carpet you pick out etc.
But, in Marianne's case, getting the carpet cut into the circle in the size she needed added another third to the cost of the carpet. Getting exactly what you are looking for, though, is worth it sometimes.
Thanks for your interest!