A bit off topic because it doesn't much address accommodations for children on board, but as departures can turn into lengthy waits with antsy children, some airports (rather than airlines) have been proactive and offer specific play areas for children. See
Children's Play Areas in Airports in this Forum.
American Airlines Admirals Club often have dedicated areas for children, including in the most elaborate enclosed areas with computers, etc. One can see which locations have those from
this page, and they are marked with a
to identify a Children's Room.
Some airlines are opposite - MH / Malaysia Airlines ban infants to age 2 in 747 and A380 First Class, and infants and children on the upper deck of their A380.