Meals would be a good start. When I was Protestant, there was a well-developed “meal train” in our church for families who’d just had a baby, who had someone seriously ill, etc. I’ve been surprised by how little the Catholic parishes that I’ve been members of have in this regard.
I do agree with the above commenter who said nursery during Mass really isn’t a great idea. Our parish tried to start a nursery recently, but pretty much no one signed up and the idea fizzled out. That suits me just fine. I just got my toddler to (mostly) behave at Mass… If he starts learning that he can play all the time if he goes to nursery, all that hard work on behavior will be all gone! And even though he’s just turned 3, he does pay attention sometimes. At home he carries around a broom pretending that it’s a cross, he pretends to do a Gospel reading, etc. So observing the Mass is making an impact on his little mind and heart – I don’t want a nursery to send the impression that he isn’t welcome in Mass yet. Now, someone to help me wrangle kiddos in the pews or at communion time? Sure thing.
Another thing is, make your cry room comfortable for new mothers. The best cry room I ever saw was at a parish I visited near OKC. It was darkened, had a few rocking chairs, and a few different pillows mothers could borrow if they needed to nurse a baby during Mass. End result – babies who had to go to the cry room calmed down quicker, and the cry room wasn’t a loud, crazy place. It also sent a message to new parents, I think, that this room was to help them and that they and their kids really do belong in Mass. It was a room to calm down in, not a room to sit and play in.