You would need to use a custom form for that.
If it’s just a date and not including the time, you can:
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Convert the chosen date to numerical value (say have a math column to convert it to MMDDYYYY).
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Do the same process in the table where you store existing reservations.
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Create a relation from the chosen date’s numerical value to the existing reservation dates’ numerical values.
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If the relation is not empty, then don’t allow them to add a row.
The process is much trickier when you add the time in, with periods of time.