You are probably not going to convince him, as his fundamental (excuse the term) UNDERSTANDING of what is involved in baptism would preclude his recognition of it in an infant.
If, to him, one can only accept baptism on the basis of the UNDERSTANDING of what it means, it is not just infants, but the mentally handicapped, who cannot be baptized. (I wonder if he has carried the thought thus far. And where he would like to make the distinction , case by case, for those with limited understanding).
With such a limited view of the nature of baptism itself, and the nature of it or any other sacrament on his part, I am afraid you’re casting pearls before swine. You’ve laid the foundation–it is now up to your friend to “let the Holy Spirit in” to guide him to a proper understanding of the truth.
It IS hard–but then again, just imagine how frustrated HE is that all his carefully “reasoned” arguments are not working with YOU either. YOU let the Spirit in. Pray for him. Encourage him in the areas where you DO have agreement–the love for Christ, for example. . .and by your example in living for the faith with Christian brotherhood, charity, and service, you’re working with the Spirit. God bless.