Speak with the town. They can assign you a number for the apartment. E911 street addresses are based on where your driveway is, so the apartment will have the same number as your house. Depending on the local protocol, they'll either call it "apartment 1" or differentiate between the house and apartment with an A and B....for instance'
201A and 201B.
Then notify the Post Office of the change if you want to receive mail at the apartment. The USPS maintains a database of all delivery addresses, which is vital to their automated sorting. In cases where an address hasn't previously existed, they *may* ask for a letter from the town. This is definitely the case with new roads....I'm just not sure about an apartment added to an existing delivery point.
I live in WA state, and we put in a legal apartment downstairs, but how can we have it's own address in case we want to rent it out?