Several of the models from Badger, Paashe, Iwata and others will do what you want. Not questioning your abilities, but the ability of an airbrush to produce fine lines is a product of the tool and the user. My airbrushes are certainly capable of doing better work than I am.
You might look into changing the needle or nozzle on your current airbrush. Some (most? many?) of them have interchangeable nozzles or needles that affect the width of the line. I was having a similar problem with one of mine and found out that it had the "Medium" tip on it. Went to a "Fine" tip and it made a world of difference.
I'm a Badger user and fan and I like my Omni. One needle, one nozzle and I can get broad coverage or fine lines with it.