If there is no reasonable assurance that after baptism the child will be raised in the faith, the priest has valid grounds for delaying the sacrament--or even refusing baptism altogether, if it is certain that the child will not receive a Catholic upbringing, something which is required by the sacrament itself. "The Church must have a well-founded hope that the baptism will bear fruit" (Congregation for the Doctrine of the Faith, Instruction on Infant Baptism, 1980).
The Church does not take the matter of refusal of the first and most important sacrament lightly. The priest is obligated to keep in contact with the family and to attempt to secure sufficient assurances necessary for the celebration of the sacrament. Once the priest is satisfied that assurances are met, such as the choice of godparents who will be diligent in seeing that the child is raised in the faith, he cannot refuse to celebrate the sacrament without delay.