Machine learning method to predict event date
You can both utilize regression and classification models in here.
Also I suggest log transform your financial features (eg: debt, last credit risk, average loan amount etc) when using algorithms except decision tree based models (since they are not affected by monotonic transformations).

Classification

You can construct a model such that predicts if a customer would pay "x" days after payment day or not. In this model you need to find best "x" by comparing results of different x day models. Also you need to find optimal confidence range in each model in comparison.

Regression

In this setting, you will predict how much day a customer will pay after payment date. Again you should obtain confidence intervals such that you calculate 3 days for a customer which means she will pay 3 days after (it can be earlier for negative predictions). However you know that your model is powerful on +2 -2 day interval. Then you should say this particular customer will pay in 1 or 5 days after payment date. 

Algorithms

I suggest xgboost, lightgbm and RNNs. But its not so clear maybe you have a linear space and it converges fast with SVMs, line fits etc. Yet they are pretty good, kaggle winner learners. 

I hope it helps. I thinks it will be a good starting point.