If there's a cycle of parent relationships, we can combine these into one big node, with cost and money the sum of cost and money of all the nodes in the cycle. For the nodes that don't have a parent, we can connect them to a (fake) root node, with cost and money 0. After this, the graph becomes a directed tree, with as root the fake node we created. I don't know what the constraints are, but if M is small and the number of nodes is too, then we could use Tree DP.

Let $$$DP[u][c]$$$ = Maximum amount of money that can be made in the subtree of node u, with a cost of c. Transitions will be, for every child c of a node u, $$$DP[u][i+j] = max(DP[u][i+j],DP[u][i]+DP[c][j])$$$.

For all states initialize with $$$-\infty$$$, except for $$$DP[u][cost_u]=money_u$$$. When done with subtree u, set $$$DP[u][0]=0$$$. The answer to the problem will be $$$max_{cost \leq M}(DP[root][cost])$$$ I think the DP should run in $$$O(N \cdot M^2)$$$, which is a bit slow, but maybe feasible.