In October, we have an overnight United flight from the Us to Madrid, arriving at 7:15 AM, then a 9:30 AM Spainair flight to Barcelona. How long will it take us to get through customs? Will we have any trouble making the connecting flight?

is it the same terminal?
do you have to collect your luggage and check it in again?

My last time in Barajas took me 1 hr to clear customs, but that was then. I don´t think you will have any trouble making your connecting flight having 2 + hrs, but I would no waste time. Any way, knowing in advance how to get to the terminal from where you will flight to Barcelona , will give you peace of mind. United arrives to terminal 1 and Vueling departs from terminal 4. That´s what I found in Google. Search for Barajas airport terminals and make your plan. Enjoy.

the OP is flying Spanair not Vueling.
Spanair flies from terminal 2 ( much better than from 4)
If the luggage can be checked through, you are o.k.

Are both flights on the same ticket? Or did you purchase separately. Hopefully they're on the same ticket as the airline is obligated to get you to your final destination. If these are on separate tickets and you need to pick up your luggage and recheck-in then it could be close.

Your problem is not Customs (luggage) it is Immigration (persons entering). these are completely different processes. the former can take a while to get from the plane to you - but then getting past customs (or if checked thrugh to the next flight - takes about 2 minutes.

If several planes land at the same time Immigration can take a while.