You will need to wait until its untapped to get more mana from it.
You seem to be under the misconception that Basic Lands give mana when tapped. This is not accurate. Basic Lands give mana as the result of using their intrinsic activated ability. Using this ability requires tapping the land, but it's not tapping the land that gives the mana, it's activating the ability. For example, using Twiddle to tap a Basic Land would not generate mana.
In your scenario, the ability that granted the mana has long since resolved. There's nothing you can do now that will change the amount of mana it gave.
And the newly granted ability won't produce any mana until its activated. To activate the new ability, you need to tap the land, which you can't do if it's already tapped.
Either way, the new ability will never grant just one mana. The instructions clearly say you add two mana to your mana pool, not just one.