Is birth control haram if you don't want any more kids?

No issue with this. Generally all forms of contraception in terms of pills, coils, implants, injections, they're all fine. The only thing you need to be careful of is a permanent form such as a vasectomy or a hysterectomy. That should be avoided because it's a permanent form or permanent change, unless there's specific medical need, in which case that would be an exception. But generally speaking, all the other forms, the temporary forms such as coils, implants, injections and so on, no issue with that.