One of our student brothers down at CUA was given the homework of asking parish priests of varying generations the following question. Even though it's poorly written, I thought I would blog my response.
One of the most difficult pastoral care situations is whether to baptize the child of parents who do not seem to be living their faith very actively. How do you handle parents who present their child for baptism, however, the parents are not actively practicing?
The situation you describe is a very common one; in fact, it is almost the majority of infant baptism requests, at least where I work. It's actually an interesting thing; I had imagined that infant baptism would be one the more enjoyable and lighthearted aspects of the parish priesthood, but I have found that is one of the most frustrating.
That being said, let me tell you my pastoral strategy. I try to look at the case as an opportunity that the Holy Spirit is giving the parent(s) to come back to the practices of the faith, to the promises of their own baptism/confirmation. I see my task as trying to 'hook' them back, to be that 'fisher of men.' Mostly this takes the form of encouragement, of seeing the birth of the child as this opportunity to get back to the Lord. But it can also take the form of a fairly stark challenge; people need to know that it makes little sense to promise a journey on behalf of someone else when they aren't making the journey themselves. All of this presumes, of course, that the parents are at least indifferent to the faith; if they are hostile or have already apostatized in some fashion, things are much harder to move forward in good conscience.
The ascetical task, then, is to stay positive. Lay on the congratulations thick, but always frame them theologically. God has blessed them, made their marriage fruitful, etc., and they should return thanks to God by prayer and assistance at Sunday Eucharist, etc. If they are not married or their marriage is not convalidated, I offer this as a next step.
All that being said in a general way, there are a couple of special situations.
1. Where I work more people are from the parish than actually in it. It has a huge diaspora. I have actually had people call me from Atlanta or LA and tell me that they are parishioners. What they mean is that they identify with the parish in a nostalgic or historical-familial way. When someone is in this condition calls for infant baptism, it is a hard case. If they have not been practicing the faith and don't even know what their parish is where they now live, I tell them that our place is not the place for the baptism. This is usually very hard to hear, but I try to explain to them that it would be nice for their child to have a church to identify with growing up too. Why deny the child what has meant so much to you? If, on the other hand, they are practicing the faith where they are and just want to come to the ancestral home for the baptism on account of family, I usually accept.
2. Sometimes it is the grandparents who are seeking the infant's baptism rather than the parents. This is also a hard case. Generally I try not to deal with grandparents, just like I try not to deal with parents during wedding preparations. Nevertheless, an involved and accepted grandparent, who is physically and mentally able to continue to advocate for the Christian initiation of the child, can be enough of an encouragement to consent to a baptism in good pastoral conscience, at least in my opinion. Again, this demands that the parents are at least indifferent to the faith and not hostile.
3. Mixed marriages can also be hard. In these cases I have come to realize the wisdom of how we do marriage preparations. Folks who have married only civilly haven't usually talked about the religious disposition of children, and the question can catch them by surprise. I have had the situation a couple of times of a Catholic married to a Jehovah's Witness, and the one parent wants to baptize the child without the other's knowledge. This can also happen in mixed marriages involving denominations that reject infant baptism.* It's also more common than you might think for the children of a Catholic-Jewish mixed marriages to be raised concurrently in both, and end up both confirmed and bar-mitzvah'd at the end of it all. St. Paul would have a blast with that, but I'm not sure what pastoral sense it makes for the soul to which it happens.
All of this isn't even to speak of the whole godparent and sponsor dramas, which are also a headache a lot of the time.
But, as I say, I look at my ascetical task in all this as being ruthless in keeping my thoughts and speech positive, and not giving in to the temptations to accusation or disdain. I always try to ask myself what the Holy Spirit wants to do for this couple or family, what opportunity is Providence giving them on this occasion, and how can I be a facilitator in that process.
*Against those who reject infant baptism, I quote the beginning of Belloc's Pelagian Drinking Song:
Pelagius lived at Kardanoel
And taught a doctrine there
How whether you went to heaven or hell
It was your own affair.
It had nothing to do with the Church, my boy,
But was your own affair.