I train on a fingerboard mostly, and climb outside quite a lot during the season (which around here is basically April-October). If you are a relatively experienced climber with good movement, then fingerboarding is the secret sauce.
Some other training ideas: your finger extensors are extremely important and making them stronger will improve your contact strength (somewhat paradoxically). There are many exercises to improve them.
Also, work your entire hand, not just contact strength. I strongly (haha) recommend Captains of Crush grippers. They don't directly translate to climbing, but they will make you stronger and balance everything out.
As for a specific fingerboarding plan: google "Eva Lopez".