Move new carriers a little bit out of the yard.
Just naval bombers and interceptors (both Level 1+) and tac bombers (Level 4+) are able to land on carriers.
Carriers must be in flight range of the planes, and you can not send groups with more aircrafts than free places there.

Only own carriers can be used, not from allies, and as any unit carriers also can be traded - but in the moment it seems there is a bug sometimes when trying to use traded aircraft carriers... ...in that case send a bug report to the support.

Can you tell us a little about your problem? What exactly?

I am not a big user of in-game aircraft carriers, but in the late rounds of a current game, I discovered the same issue: aircraft would not land on a carrier in port. I have no idea whether this is a bug or intentional programming, but there is a logic to it. In the real world, current carrier-based fixed-wing aircraft cannot safely land unless the carrier is underway and headed into the wind -- it's necessary to reduce the relative speed of the aircraft to that of the carrier, while still maintaining sufficient airspeed and lift to avoid stalling on approach. While WW2-era propeller-driven aircraft were smaller and lighter and had lower stall speeds compared to modern carrier-based jets, they faced similar challenges in landing on a stationary carrier, and new aircraft were usually hoisted on board a carrier while in port.

Bottom line: the solution above is easy enough and does not seem to present any additional problems.

Makes a little sense I guess, Carriers do need to be out at sea in order for planes approach paths to be clear at such a low altitude. So they probably wouldn't be landing or taking off while docked anyway. They don't drive the planes up a ramp on the boat do they? They send the carrier out to sea and then they land the planes on it.