In the first instance, both Vatican and many American dioceses reiterate the principle that the most appropriate time for infant baptism is the Easter Vigil, and secondarily most Sundays of the year, including the Christmas season. The only reservation appears to be the Lenten season, where several dioceses discourage the practice in favor of waiting until the Easter season. (As one might expect, in cases of grave illness or danger to the infant, the time and place of baptism is at the discretion of the pastor or even laypersons and our discussion here would not apply.)
Just about all of the commentaries on infant baptism talk about the appropriateness of celebrating the sacrament in the context of the Sunday or Vigil Mass. The general reasons appear to be twofold: the first is the unity of the sacraments of initiation, intimate connection between baptism and the Eucharist. One diocese observed that the application of weekly attendance at the Eucharist actually begins with infant baptism and offers a number of pastoral suggestions on how this might be done. The second reason generally expressed is the appropriateness of a family presenting a child for baptism surrounded by its regular community of family and friends in faith. I think that a third consideration is the obvious catechetical one of awakening understanding of the ongoing power of baptism and the attendant responsibilities in the general congregation that participates.
The rules and guidelines do not insist that all baptisms take place in the context of a parish mass on Sunday. I have considerable faith in my own parish that this determination is made in congenial conversation with the family regarding the decision to celebrate the infant baptism before the large numbers who attend weekend Mass . In other circumstances I have come across pastors and (more likely) pastoral associates or volunteers whose approach to pastoral sensitivities are sometimes one-dimensional, who take a "one-size-fits-all" approach to liturgical and pastoral circumstances.
For example, anyone who has worked in parish ministry for any length of time is certainly aware that many parents who come forward to present a child for infant baptism are not themselves practicing the observance of the Catholic faith in the fashion we might hope for. Both Vatican and local guidelines give considerable attention to this. One point is clear: no parents, and no infants, are to be summarily dismissed based solely on past performance. The guidance appears to assume that the child is innocent of the deficiencies of the parents and entitled to the saving waters of baptism. Just about every document I reviewed called for a Catechumenate – like faith orientation for fallen away Catholics. For our purposes here, the question would be the length of such a discernment process vis-à-vis the amount of time between the birth of the child and its baptism. There may be cases where parents are not ready to stand at the altar in full communion in the celebration of their child's baptism at public mass, and yet there is no need to delay the child's baptism unduly. In such cases a more private alternative celebration of baptism may be more appropriate, depending on pastoral judgment of the pastor and formation team.
Similar to the above cited situation is the case of parents whose marriages are not blessed in the church, who are living in what we often refer to as "an irregular situation" and ipso facto unable to receive the Eucharist in their current situation. I am assuming that part of the faith formation of such a couple prior to baptism will include a discussion of their marital situation and the possibility or probability of undertaking the annulment process or processes. The law as I read it does not forbid the baptism of infants whose parents are not married in the church, again based on the grounds that the child is something of an innocent party fully deserving baptismal initiation. Even with all the goodwill in the world, parents in these circumstances may find that obtaining an annulment and having their marriages blessed or convalidated in the Church may take some time and this circumstance will conflict with the canonical directive that infants be baptized reasonably soon after their birth. It would be a hard thing to expect of parents in an annulment process, for example, to stand before the public in a Sunday Liturgy when they are not yet able to receive the Eucharist in full communion with the assembly.
There are other interesting and important guidelines to note as well. It is consoling to note that a number of pastoral directives make a point of stating that a single mother may present her infant for baptism, so long as her general faith intentions are good. In one diocese I came across a very interesting pastoral consideration. This is the case of two same-sex parents who are civilly married in one of the many states that now permit such marriages, and present an infant or young child for baptism. The couple would be legal guardians either by natural birth or adoption. The advice given by one diocese on its Internet site indicates that if at least one of the adult parties gives evidence of the normal prerequisite faith disposition, the child may be accepted as a candidate for infant baptism. This is a new area of pastoral consideration with multiple implications, but again the spirit here is the spiritual benefit to the child.
A number of diocese also make the point that there are many people who are by disposition shy or introverted, for whom standing before an assembly of 1000 congregants or more would be a psychologically stressful ordeal. For all of the circumstances noted above, I think it is fair to say that the wisest pastoral course of direction is the offering of multiple options for the celebration of the baptism of infants. Clearly, the public Sunday observance enjoys the greatest support of theology and law, but Vatican and local directives seem quite open to the multiplicity of pastoral considerations. The celebration of Baptism is one of the greatest opportunities for evangelization in any church, and accommodation to the needs of family and parents creates a goodwill that extends far beyond the rite itself.
I am including here the Diocese of Richmond's instructions on the baptism of infants for its clarity and excellence.