Almost every all inclusive resort that welcomes families offers a kids' club, but often these are only for ages four and up. Parents of younger kids can probably arrange for a babysitter... Or try one of the resorts, below, that have nurseries or baby clubs.
Club Med Ixtapa Pacific: a top all-inclusive family resort with terrific kids programs including baby care; on Mexico's west coast, near Zihuatanejo, about 100 miles north of Acapulco. Baby Club takes ages 0 through three years, in two age groups. ( Baby Club Med isn't part of the "all-inclusive", though.)
These all inclusive resorts in the Mayan Riviera have special programs for kids under five, created with toy company Fisher Price, and lots of complimentary gear for babies. One resort has a parents-participation activity center for 2 to 3 year olds. Kids clubs too, for older kids. AZUL by Karisma signature features include: 24-hour room service; beach butlers; "gourmet inclusive".
Baby Club takes ages 18 months to 3 years. This resort has many features for families, including supervised children's waterpark. Click for a profile, for families.