As a general rule of thumb airlines do not ban children from any level of service, they will sell tickets to anyone with the cash. My daughter has flown in business class on several airlines without issue and I have seen plenty of kids in business and first class on all the airlines I fly.
There are likely some destinations served where cultures keep children separate from adults or relegated to a lower status. On routes serving these destinations, some airlines may try to keep children out of the upper class, to keep the local business travelers who frequent the route happy.
And I know some airlines have tried to introduce quiet zones, by banning kids, but boisterous, non-stop talking adults are just as bothersome as the kid who cries occasionally.