We study coordination of assembly systems with random supplier yields and random customer demand. We propose four contracts which are combinations of well-known contracts in the literature and show that the contracts can coordinate the chain under forced compliance. Our contracts have less payment schemes than the existing contracts given for coordination of assembly systems in the literature. We show that arbitrary profit allocation between the levels of the supply chain (the manufacturer or the suppliers) is possible. We also provide sufficient conditions which enable arbitrary profit allocation among the suppliers and illustrate the profit allocation with numerical examples.