The main problem in our area growing any type of fruit tree is that we keep forgetting to turn the tap off and so it rains all the time!! In a pot the size of a half whisky barrel you could grow the following. Make sure they are grafted onto dwarfing root stock such as M9 M26, M27 or Pixy and then they won't bolt on you. Make sure you stake the tree because the dwarfing union isn't all that strong, place a mulch on the top and use a slow release fertilizer such as Osmocote 14-14-14. Then sit back and enjoy the tree. Why not try a pomegranate or a persimmon? A Dolgo crabapple or a Stella cherry? Place annuals all around the base with smaller spring bulbs growing through. Very classy.

Columnar apples are excellent choices for containers. And while not really trees, so are blueberries. But neither are very 'exotic' :-) Dwarf citrus also do well in containers but need some sort of winter protection. Perhaps placing your container on a dolly or attaching heavy duty casters to something like the half whiskey barrel would facilitate movement.

Any of the dwarf or minidwarf fruit trees should do well in large containers. Check to see if your choices need a second type for pollination. There's a number of different exotic fruiting plants typically available at local nurseries and seem to be more available each year but most of these tend to be shrubs or vines rather than trees.....maybe you might want to consider enlarging your choices.

The other consideration with growing fruit in small spaces is to espalier the various trees. It takes some time for training and attention to pruning but you can get a lot of different trees in to very small spaces this way. You could actually construct an espaliered fence around your backyard.

Meyer lemon works just fine in a pot.