Please note that all databases depend on public records compiled in such a way as to make them searchable. Not everyone can be found in a database. Look to see where each place is getting their information.
Common names bring back way too many returns.
A range of age search is never as good as an exact DOB search. If you do not have a name to use in an adoption search the following websites can not help you. There are some people who do have birth indexes and they are the ones you should contact if you can pay to get the name. Not all states have birth indexes available. Colorado searches mostly through the State CI program.