Yes, you need an unlock code for every GPS you want to load City Navigator onto. The maps are unlocked for your old GPS and you need a new unlock code for your new GPS.
Did you register both units on the Garmin website?
Contact Garmin (a Toll Free call in the US) and explain your situation. They should (might) give you an unlock code for the new unit. When they replaced my GPS a few months ago it only took a few minutes on the phone to obtain a new unlock code to transfer my maps.
Thanks I will call them on Monday.