The use of the plural 'persons' is only for formal contexts. You might see it in legal contracts and official notices, for example. We never use it in everyday or spoken English.
So, for example, you might see a sign in an elevator (lift) which says 'Maximum capacity 8 persons'. But you would never say this : in speech, and in ordinary written language, you'd say something like, "You're not supposed to have more than eight people in here."
And getting back to your original question, if you're asking for a table in a restaurant, you'd say that you want a table for two people. Or, as Andrew says, simply a 'table for two.'