You can't put UL on it without submitting it to UL for testing and approval. There are other available services such as CSA, ETL, METLAB, TUV, etc... that can test to UL standards and allow you put their own logo on it. My refrigerator, for example, has CSA mark for electrical safety.
I assume your clock plugs into the wall (120 VAC). In that case, you really need a safety listing or it's going to be hard to sell. Most retailers won't accept it. If it's battery powered, it isn't necessary to list it.
If it is a digital clock and contains any signal that pulses at greater than 9 kHz, it is illegal to sell without FCC verification testing, whether battery powered or not. You'll have to get a lab to do that. Get a copy of FCC 15 Part B (it's free) and read the section about unintentional radiators very closely. You haven't told us enough about how your clock is powered, but it really needs to be your call anyway. There are some exceptions in there, and you might qualify for one.
Check these things out thoroughly. Also consider posting this in the UL Code Issues forum, and post a link to it here so you don't continue to get answers in this thread. The NEC has nothing to do with end-user products.
You might need to hire an EE with product compliance experience to guide you through it.
Good on ya,
Goober Dave
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