Sometimes it's a struggle to catch back up, but the only thing you can do to directly get dwellers more quickly is get your dwellers to make babies. Other than that, just try to get your shelter back to operating as well as possible, as well as having room for more dwellers to come by.
You can also have a certain room that you can assign a dweller to that will let a dweller use a radio to call out for more dwellers. You have to have 20 dwellers before you can get the room.
