Unlike the Fuchsia City Gym and the Saffron City Gym, the Cinnabar Island Gym shouldn't be all that difficult to defeat. To start, if you answer all the questions correctly during the game show portion of the Pokemon Gym, you will only have to face the Gym Leader, Blaine. Even if you don't answer every single question correctly, all of the trainers found within this Pokemon Gym will own nothing but Fire Type Pokemon.
These Pokemon shouldn't be very difficult to overcome, especially when you consider that you have to surf to reach Cinnabar Island and that the seas are full of Water Type Pokemon that Fire Types are extremely weak against. Furthermore, back in Fuchsia City, there is a Move Tutor that will even teach your Pikachu Starter Pokemon a Water Type Attack of its own. A couple of Water Types, as well as your Starter Pokemon knowing its own Water Type Attack, should be all it takes to defeat this Pokemon Gym.