How is the best way to keep tree roots out of your garden? Would it be wise to dig out about 16″, line it with plastic sheeting (using a 4 mil plastic and no seams), and fill it back in, leaving a drain hole at one end?
Really, there is no sure-fire way to prevent tree roots from spreading out into the garden other than planting the garden well enough away or installing raised beds,which I would recommend. Rather than put all your time or money into something that may not guarantee success, you might want to consider implementing some raised beds for you garden instead. Of course, it also depends on the tree, as some of the smaller ornamentals and fruit trees do not have overly extensive root systems.