Ask the cousin for details and evidence of the loan — how much did he lend, when did he lend it, what was it for. what was the understanding about repayment? Ask if there was evidence in writing. Ask him to produce bank statements showing the payment out of the money to your dad. Explain that, as your Dad never told anyone about this loan (whereas he did tell people about the loan from your sibling) you will have difficulty paying it out unless it can be documented or evidenced.
Also ask yourself (and your family can ask themselves) whether, from your knowledge of your father, it is likely that your father would have borrowed money from his cousin and told no-one about it.
Your mother's duty as executor is to pay your father's debts, and you have to give creditors the chance to establish the existence of the debts, but it is up to them to establish them. In the end, you consider whatever the creditor produces and you decide whether it establishes that, more likely than not, your father did borrow this money. If so, then you repay the money. If not, you tell your cousin that you don't feel able to repay it and you give him an opportunity to take the matter further (i.e. institute court proceedings) before you distribute the money, if that's what he wants to do.