Yes, the Layaway & Partial Payments Extension for Magento 2 supports COD. But with this option, admin is required to manage the installment payments manually.

Read this guide on How to Sell Products on Installment & EMI in Magento 2 Website to setup this extension.

Here are the few more resource to help you get most out of this Magento 2 Partial Payment and Layaway & EMI Extension.

• What are Layaway and Partial Payments? How is it Beneficial for Businesses and Customers
• Drive Customer Loyalty through Layaway & Partial Payments
• How to Reduce Abandoned Carts with Partial Payment Extension
• Enhance the Customer Satisfaction Rate with Partial Payment Extension