Congratulations Zeus'Dad! :D Mrs. Zeus'Dad too of course ;)
I have just a little experience in this area....6 times. LOL :)
This is only my method; and I'm certain there is a web site or a hundred that is out there to help as well.
When I bring my baby (or babies as has been the case twice) home...I keep the baby in the carrier/carseat and position it on the couch. (that's the same couch that my dogs are not permitted to be on.)
I then invite the dogs, one at a time to sniff, smell, look at and investigate this new being. (The whole time I'm sitting RIGHT NEXT TO THE BABY, talking in a soothing tone to the dog, and reinforcing "eeeeeeeasy...niiiice baby" while using a stoking petting; NOT patting.)
Never, ever do I allow the dogs to be with the baby; EVEN in the baby's bedroom if I am not there. (The cry of a newborn baby is very much like dying prey. If a dog has never been exposed to the strange noises babies make; this is something that could easily confuse them...and even frighten them.)
This is a daily ritual. It doesn't take long for the dogs to almost get annoyed that I keep calling them over..."Yes MOM...we get the picture...it's a BABY and it's STAYING...I'm going to go back over here and nap if it's all the same to you!" :)
One other thing...
Expect Zeus to be VERY happy to see your wife since he hasn't seen her since you wisked her off to the hospital :D I would suggest she come into the house (leave you and your new bundle of much joy in the car for a few minutes) just so she can say hello to him and help him through his initial "OH you're HOME! Yipeeee!" thing.
Have her put him in his crate or another room behind a closed door so you can bring the baby in....set up....and get his leash.
Depending on his level of training (and if he normally does NOT jump on you or your wife....or the couch
) I would leash him, just as an added little precaution.
I've honestly never had any problems introducing my adult dogs to any of my children....in fact...my Aik (GSD) is the one who told me I was pregnant with my 6th! He would lay his big German head in my lap and nuzzle my abdomen. Very unusual behavior for him. He's a pet-n-go dog...no real cuddle bunny.
Maybe it's a K9 6th sense :)