At the moment I can think of:
- Keeping in contact to see how they're getting on, but understanding if they're busy and can't talk.
- Offering help with things like shopping and chores.
- Offering to baby sit so they can relax for a little bit.
- Buying things like baby clothes and other baby things.
I can see lots of advice for new parents, but just not sure if there's anything else I can help with. Obviously don't want to be overbearing either.