I don't think there are any issues specific to Central with this. I recommend reading through some threads like https://security.stackexchange.com/questions/121163/how-do-i-run-proper-https-on-an-internal-network and https://serverfault.com/questions/964119/enable-https-on-a-private-network to get a feel for the challenges and possible approaches.
I think it's also possible to get a specific Android device to accept a self-signed cert following instructions like these.