I cannot make circles either. This is my method for the center of my Dresden plates that may work for you too.
First I find a cup, bowl, saucer, lid, etc. to use as a pattern for the size I want.
I trace it on the smooth side of light non-woven interfacing with a colored 'sharpie' to match the circle fabric (just in case it 'shows' through).
I then layer interfacing and fabric, (right side to bumpy side) then stitch the circle slowly, following the line I drew.
When finished sewing, trim fabric about 1/8 from stitching around outer edge.
Make a slit in the interfacing near the center. Turn right side out.
Now you have to decide if you need to trim most of the center away, or work with it in place. For hand applique I leave it in, then trim it CAREFULLY away from the back after sewing, but for machine applique I trim most of it away leaving about 1/4 inch around. Iron in place, than stitch using method of my choice.
I learned this from Eleanor Burns. Works for any circle size.