No dwellers will come to my vault and I don't have enough dwellers for a radio tower. I tried babies but it takes too long. How do I fix this?
There are only those two options: First, make babies. Second, wait for random people to want to join. If you don't have enough for a radio tower, then I assume you don't have enough for an overseer's room (I can't recall offhand how many dwellers that takes) because there it's possible to come across people in the wasteland while on a quest from the overseer's room, and invite them back to your vault, but that's even slower than making babies. Find a couple people who have 100% happiness (they will mate faster) and make sure they're not already related (zoom in, and if they talk about spending time with family, swap one out for another dweller) and just wait for the famous yellow-shirted pregnant dweller to come strolling out.
I try to do that before I turn the game off, so the baby will be ready to be born as soon as I start playing the next day.