Back out the the trigger adjustment screw by turning it counter clockwise about 1/4 turn at a time then check it again; repeat until it works satisfactorily, and the hammer remains cocked with the barrel installed.Then back it out another 1/8 to 1/4 turn for safety sake. If the action is an "easy open" action, this trigger adjustment screw will be at the top of the trigger, and appear to go into the action. If it is a pre- "easy open" action, the screw must be accessed from inside the action, preferrably after removing the barrel. Turn the screw out (counter-clockwise, also) that same 1/4 turn at a time and repeat as necessary. You may also have to back out or adjust the trigger overtravel screw in the back of the trigger guard at the time you are making these adjustments.
T/C furnished a small allen wrench with each Contender just for this purpose. I believe that the size is .050", but I don't have one in front of me to measure.
Any hardware store should have this size. Just take the action with you to check, if necessary.
This is a very simple adjustment. The newer G-2 Contenders do not have an adjustable trigger, so none of this applies to them.