It will be tough to treat without tearing up the floorboards. Insulation between the joists will likely help some, as will adding more mass to the floorboards (please have a structural engineer check out your plans before you add mass beyond what the structure can handle).
For dimensions, you can look at room mode calculators: RealTraps - ModeCalc
In general, make the room as big as you can, and make sure no 2 dimensions are the same or even multiples of one another. If you do this, and treat the room well, you'll likely be pleased.
More on treatment here: RealTraps - Acoustic Basics