1 ton would be the smallest for a ductless. It is not about the loss, but also the heat gain caused by the equipment, in how much btu that it is putting out, along with factoring in how many people are in the room at any given time. You could probably compensate with the 1 ton, if you had to include say a bathroom, or a home office or such. Also have to factor in, how air tight the existing home that the home theater is going to be placed into at that time.
So overall, a 1 ton may help overall, when it comes to the existing system, in cooling the home during the Summer months. The good thing is, you could set up a zoned system, that if you know that no one will be using the space for say a week or a couple of days, you could use the new system to help the existing also.