I'm the family cruise editor here. I wasn't sure if your question is which lines allow infants under 4 months aboard or if it's which lines accept babies under 4 months in a infants' and children's program? Let me know so I can help you out better. If it is the latter -- which lines have a program for those under 4 months -- yes, Disney is the only one with a nursery program (hourly fee) for babies from six weeks to three years. We checked out with our baby last year and felt it was excellent. See my article on this section of the web site on Disney's Nursery program.
Smooth sailing,
Luisa Frey Gaynor
Family Cruise Editor