Congratulations on the new member of your family!
Many children are not baptized in the traditional white outfits. But apparently this means a good deal to you, and that's fine. I did that, and my husband didn't understand either, but he didn't object as long as it didn't go over budget (well, sometimes it did, but I covered the rest of the cost).
As you already have recognized, christening outfits generally are in small sizes. That's what the manufacturers do.
You could go to Macy's or another upscale department store and see what's available. Talk to an experienced (!) sales clerk about your situation. If she doesn't think anything is available in that store, ask her for other suggestions.
Think about having someone other than your mother make an outfit. Is that possible?
There are online sources. I have no idea what the quality of the clothing would be, but here are a couple I just noticed when I googled:
http://www.catholicfaithstore.com/Store/Products/Cat/518/...
http://www.christeningshop.com/boys-outfits/christening-o...
They look a little pricey, but if you could fit it in your budget, you can think of it as something to give your son for when he grows up and has children of his own.
For what it's worth, for various reasons our second daughter was not baptized until she was about ten months old. So she couldn't wear a newborn outfit, either. I bought some pretty fabric in a pink and white floral print and made her a simple dress, by hand. The "by hand" part was so it could be special (and it was doable because it was a wear-once outfit). Of course, it's easier with little girls! I don't know if I could have made a little boy's outfit!