It is very difficult to prevail on a verbal contract with these facts, because there can be a slight difference in the facts of the contract, which can change the outcome.
For example, he could say the repayment terms were that he had 3 years, then what can you prove?
Before filing a lawsuit, you should have more proof to be able to prevail, such as could be by exchanging documents that better show the terms. You have two years to bring an oral dispute to court in Texas.
Perhaps he will be in better financial condition, or will honor the loan if he knows how difficult it has been for you.
General legal advice is offered for educational purposes only. A consultation with a qualified attorney is required to determine specific legal advice as to your situation and applicable law. We are a debt relief agency and we help people file for relief under the bankruptcy laws.
While I do not disagree with sole attorney answering the question previously, I do believe that you should contact an attorney who is willing to listen and review any and all documents related to this transaction. I agree that not executing a promissory note leaves this in the arena of oral contract, which are harder to prove.
Any communications via emails, letters, or invoices received from or sent to your cousin could bolster the fact that this was in fact a note/loan. Consult an attorney with experience in contracts and collections for further guidance.
In Texas, we tend to find that a contract exists when money or services changes hands. There are several causes of action that can get your money back, or a judgment that the money is owed, at least. Put together a chronology that is as accurate as possible and visit an attorney. It may be that a small claims court proceeding is the best way to go, or it may take a full suit that needs one of us to assist.
I'm not your attorney; my answer includes assumptions. If you want me to be your attorney, I'm easy to find.