In general, your goal should be to find an approximate gauge match, not try to find a pattern that exactly matches your gauge.
Patterns are generally written for a type of yarn. Basically you want a pattern in a sport weight cotton.
Check out Elann.com's pattern search
These are generally "for purchase" patterns, but it might get you going in the right direction.
Once you find a pattern appropriate for your yarn, you adjust the gauge by changing needle size.