Is it possible to customize the activation function in scikit-learn's MLPClassifier?
Although @Emre's comment that sklearn wasn't specifically made for the task is correct, nothing stops you from introducing another activation function by implementing it in sklearn/neural_network/_base.py. You should be able to find the file in your installation.

To this end, you would define your single-parameter function and add it in the ACTVATIONS list. Refer to the existing implementations for some guidance how to do it.