I am trying to find a female person born in 1941. I have a last name and birth place city only.

It was possible that she was born in 1940 so I looked through the Census from 1940 but could find nothing, so she must have been born in the first couple of months in 1941. Problem is I can't seem to figure out where to start since there is no census beyond 1940.

New at this, so any help or tips you can provide would be appreciated. Thanks!