If you don't wish to start over (spent too much on the current vault, or whatever reason), you can do several things:
The radio room: Yes, it will take a while, but basically, it's your best bet. At this stage, look at how long it'll take to call a new dweller, and quit out of the game, and reload the game when that timer runs out. This will avoid any extra havoc caused by Raiders or Radroach attacks. There is also a chance that a dweller will just randomly appear, and I believe the number of dwellers can affect this (less dwellers = higher chance of random dwellers arriving).
Quests: this is risky, because it leaves your vault under-manned. Occasionally, quests will give you the opportunity to get extra dwellers.
Some things to remember:
- All you need is one Male Dweller. once you have one male dweller at least, you can effectively double your population. From there, it becomes a delicate game of balancing who's related to who, but you should be able to get a few more generations out of that.
- Don't remove dead Dwellers. You can revive dead dwellers! At a price of course. Yes, leaving corpses lying around can heavily affect your vault happiness, but if it means the difference between an unhappy vault, and a heavily under-manned one, I'd suggest dealing with a few unhappy dwellers for the time being. You can always raise their happiness later!