If my ex wrote a letter agreeing to pay me a certain amount each month and said he would have it notarized. will it hold up in court?

If this was a loan, then it would be enforceable--any loan agreement in writing (and most that are oral) are enforceable.

If it was not a loan, then it may not be enforceable. A "gratuitous promise" is not enforceble, even if in writing (the notarization doesn't add anything); for a promise to be enforceable, there must be consideration for it, or something of value given in exchange for the promise. However, you write that you are unmarried--that means, for example, that you do not have a right to spousal support, so you are not giving up any potential support as consideration for this agreement.

To make the agreement enforceasble, therefore, there must be something to which you have a right, which you are giving up; or there must be something else of value, which you are providing. For example, say you and he jointly bought property or vehicles and you let him have them--that could be sufficient consideration. Of if he used your credit card, but you agree to forego a claim for that in exchange for payment as per the agreement, that might be enough.

In short, if it's a promise given freely--gratuitously--without your ex receiving anything in return, then since you were not married, it is most likely not enforceasble.