Facing yield uncertainty is a common phenomenon that corporations encounter in their production and operations processes, especially small and medium-sized enterprises (SMEs). It is a challenge for SMEs that also have capital constraints, and thus financing from supply chain members or commercial banks is the normal way to improve the efficiency of supply chain operations. We consider a supply chain finance system consisting of an SME, a core enterprise (CE), and a bank, in which the SME is capital-constrained and faces productivity yield uncertainty. Therefore, the SME may use two financing sources to support his production: financing or advance payment from the CE. In the presence of bankruptcy risks for the SME, we model their strategic interaction as a Stackelberg game with the CE as the leader. We design the framework for the order penalty contract and derive the optimal strategies that include the planned production quantity decision of the SME and the pricing decisions of the CE under the two financing sources. We find that from the SME's perspective, he will always prefer advance payments from the CE to bank financing. Furthermore, we propose a framework for partial credit guarantees. When it is difficult for banks to evaluate the credit history of SMEs, CEs provide guarantees to banks for financing SMEs. The analytical methods and numerical results provide decision-making methods and suggestions for production planning of the SME and wholesale prices formulated by CE.