In the Church of England, Baptism is normally administered on Sundays at the best-attended act of pubic worship, so that the congregation may witness the newly-baptized being received into the Church (see Canon B 21).
I know we're a broad church, but I've never yet held an act of 'pubic' worship, and hopefully never will. Baptism is clearly not the only thing that would be witnessed at such an event, but I'm not even going to go there. If the devil does live in Church House, then I think I've just found him in the spellchecker.
(For the record, when couples come to be married and already have children, it is a good idea to include them in the marriage service. However, if you're creative with the service itself, I'm not sure a whole extra section is needed to offer thanks for the gift of children. The prayers already cover that. It would be good to hear a bit more from Tim Sledge, quoted in the CofE main article, about how a combined marriage/baptism works. I guess at the very least it lowers the carbon footprint for clan gatherings - 1 instead of 2.)