While most work on differential privacy has focused on protecting the privacy of tuples, it has been realized that such a simple model cannot capture the complex user-tuple relationships in many real-world applications. Thus, user differential privacy (user-DP) has recently gained more attention, which includes node-DP for graph data as a special case. Most existing work on user-DP has only studied the sum estimation problem. In this work, we design a general DP mechanism for any monotonic function under user-DP with strong optimality guarantees. While our general mechanism may run in super-polynomial time, we show how to instantiate an approximate version in polynomial time on some common monotonic functions, including sum, k-selection, maximum frequency, and distinct count. Finally, we conduct experiments on all these functions and the results show that our framework is more general and obtains better results in many cases.