I cannot speak for other Denominations, but the Church of England will accept that ANY Christian may baptise another person if there is a danger or belief that the person might die without.
Catholic Church: "In imminent danger of death ... when no priest or deacon is available, any member of the faithful, indeed anyone with the right intention, may and sometimes must administer baptism"
(Rite of Baptism, No. 16)
My mother-in-law, a Roman Catholic, was told by her priest that she could baptise my baby son, her grandson, herself, by taking a little Holy Water from the Church and carrying out a small ceremony. This was not dependent on my son's health at the time.
I wanted both my children to make the choice to be baptised into the Christian Church if they chose to do so, and therefore my son had not been christened (and neither was my daughter).
My mother-in-law incautiously told me that this was what her priest had said, and I told her that we, as parents, strongly disapproved. I respect others' religious views, but if a religion states a baby is condemned to Limbo, a dreadful place, if not baptised, then I question that religious statement and urge adherents to do the same.
However, my son and I have always wondered whether he was 'done' on the kitchen table whilst I wasn't looking.
I am glad to hear Heywood's comment that Limbo is not now part of Catholic teaching.
