You might have really screwed up his green card prospects by using his tourist visa. I hope it's not too late to remedy the situation. What is the immigration status of the other parent?
A child born outside the US to a green card mother can instantly obtain LPR status at the port of entry. The conditions are that the child must be under 2 years old when entering the US for the first time, and the child must be accompanied by a permanent resident parent who is entering the US for the first time since the birth. No visa is required.
If those conditions were met when your son entered the US, it may be possible to contact CBP or USCIS with proof of those conditions and get them to change him to LPR status. If he was accompanied by an LPR parent, they should have noticed that and ignored the tourist visa, and given him an I-551 stamp in his passport. So this would be their mistake as well as yours. You might be able to convince them to correct the situation by pointing out that they made a mistake.
Or maybe they gave him an I-551 stamp and you don't realize it. Look in his passport to see what they stamped.
If that doesn't work because the conditions were not met at the time of entry, or CBP/USCIS refuses the GC because a tourist visa was used, then he will be here illegally once his I-94 expires. So you or his other parent will need to become a US citizen and sponsor his GC the regular way.