What DC motor controller will work for a small toy train?
The only difference in current draw with a 1.5V supply vs the 1.5V battery will be due to the difference in output resistance of each. Which is higher will depend on how the supply is designed.

However, since you want to drive this train faster without burning out the motor, you really want to use a current limiting supply. 

If you can measure the typical stall current of the motor at 1.5V and build a driver that limits the current to under that value while being able to drive up to 9V, you should get the thing spinning around quite nicely with minimal over-heating. The brushes will wear faster though.

However, since you are looking for a prebuilt solution, this does not really help you, and unfortunately, we can not suggest devices here.