Other than the obvious fact you brought an innocent baby into the world with a toxic babydaddy, you sound way too smart to fall for this.
Toxic people, especially guys, love using suicide threats as a way to manipulate their partners to do what they want. It's not even original. Same with his nonsense words about loving you, etc. He doesn't really want a relationship with you out of love or whatever. It's gameplaying and control.
He's doing this because he thinks it will work. It probably did in the past. So you have some hard thinking to do. Good co-parenting is important, but if his life plan is to use it as a weapon over your head, this will destroy your attempts.
I don't know what to suggest, but I do know you want to start keeping a diary of his behavior and words. Also, you do need to be VERY firm that he's to stop bringing this up. However, if there was any violence involved, or you think he's capable of it, this opens up a whole new problem area. Once he realizes you won't be manipulated, this is when toxic guys can go nuclear, meaning you and your baby are at big risk.