I think there are a couple of things you could do that are appropriate.
First, you could produce a cigar (possibly a chocolate cigar) to give to a friend. Cigars are (were) common to give out in celebration of a newborn baby. At least, I knew people that passed out chocolate cigars. You can make the production very quick, and move on to talking about the important things about the baby, like how the baby and mother are doing. I think the cigar productions are described in a lot of places. John Carney describes an entire routine that begins with pulling a cigar from a very small coin purse--using just that production may work.
Next, you said that you want to announce the birth. Maybe some sort of magical card? I'm not quite sure here, but a card with an optical illusion, or something clever about it, but not so clever that it takes away from the birth announcement.