A diode allows current to flow in one direction only; if it's doing that for one doorbell and you add a second doorbell, the diode should function for both or malfunction for both. These things also draw very little current so a larger transformer does not seem to be indicated.
Try reversing the plus and minus at the second doorbell. This is just a stab in the dark but worth trying.
Try drawing up a schematic so we can see how the thing is connected, or give us a URL to a manual on line, showing us which connection scheme you're using.
A good answer is easier with a clear question giving the make and model of everything. "The biggest problem in communication is the illusion that it has taken place." -- G. “Bernie” Shaw
