Can a 2 month old travel from Canada to the US by air without a passport?

I have a 2 month old baby that was born in Canada. Both my husband and I are Mexican with Mexican passport and visas.

We need to go to Mexico on family business but the baby doesn't have his passport. We just registered him a month ago. Is there any way that he can travel by air only with his birth certificate?

I'm sorry to say that due to new travel regulations all people (even 1 day old babies) need a passport to travel. The birth certificate alone will not help you. If you are mexicans go straight away to the mexican consultate and ask for an expedited passport for your child. This could be the quickest way as you are both mexicans although the child was born in Canada. He will also need the Canadian passport but maybe getting the mexican one first is quicker. Anyway I would try with both agencies and see which one comes first.

I don't think so.

nope not at all w/ law changes. One way around it however, if you are close to an american border. Drive across (you do not need passports to drive still) Then catch a plane from a US city to the closest (San Diego) city to Mexico and again drive across. Once an foreigner is IN the us legally they do NOT need a passport to fly back and forth w/in the US.
This is a fact, my cousin is here right now w/out passport. She used her DL and BC to drive across and just flew out to visit more of our family on the coast.
(She is from Canada)

Carry on luggage.

The rules aren't static. They keep changing their minds. Starting January everyone required a passport to fly international flights. Then at the end of February they announced birth certificates for kids would be sufficient. BUT my reading of that change is that it comes into effect sometime next year. Best to contact the embassy to double check - it might be allowed. If not, I believe you are in the Toronto area, you could book your flight from just across the boarder as a birth certificate is good enough for a land crossing. Or are you stopping in the US? A direct flight from Canada to Mexico might be the most lenient route.

Edit: I re read the rule, kids will only be able to travel by land and sea with a birth certificate, they need a passport to fly.

Not under the new regulations...everyone needs a passport to travel by air to the US.

You need a passport for the baby - if you have birth certificate for the baby then you can apply for a Canadian infant passport.