Why is it required that this phrase is used when announcing someone's latest veiny loin-extrusion? Is this some long-written social statute?
"Jack and Jill McBreeder are now the proud parents of a bouncing baby boy."
This never sounds cute or even remotely plausible. It's a newborn. It's lying flailing and screaming in a puddle of its own excreta. Hell, even if you dropped a newborn, it'd be unlikely to bounce. Unless you dropped it onto a trampoline, I'll concede, but I don't think very many new parents do this and if they did, I doubt they'd want it announced.
Is it the buh-buh alliteration that you like? Why don't you just cave and say it in full-on baby-talk to more properly satisfy your insufferable fawning urge.