What is the ideal size to a binary CNN? Is my dataset long enough? I would like to know what is the ideal size to a CNN, or there's a mathematical function to determine it, or it change through the differents scopes? 

And also, I'm doing a binary classification CNN with 700 images each class(total - 1400). Is it too small? How could I argue that it is small?

Note: I get 83% accuracy with my cnn.
There is no mathematical function that is able to relate size of model and performance.

Architecture(filter size, activation, depth, weights initialization) of a neural network can be thought as hyperparameter and hence to improve your model you need to employ hyperparameter tuning methods.

The other way to improve your model is to experiment with state-of-the-art features with your architecture. I believe your dataset being small enough give you a lot of room to experiment(because of the supposedly fast training time).