The custom report can be used to give you close to what you want. Chose the Selected individuals option. I selected the Birth vital fact and searched on Contains 20 July. The report listed all births that occurred on 20 July. Unfortunately it also selected any year that contained 20, 1820, 2005, etc. In my case all the extra entries were for 1820. I then filtered out birth date contains 1820 and had only people born on July 20.
Cumbersome but this is all we have right now. Maybe you should request FTM add a historical report that allows you do list all events in your file that occurred on a certain day and month.
Curt