Roll each biscuit somewhat flat (not going for prettiness or evenness since we are making dumplings). Slice each rolled biscuit into bite-sized strips. In a dutch oven, combine the peaches, juice, milk, Splenda, and butter.
Heat over medium heat just to boiling. When the mixture begins to boil, drop the dumplings in one at a time. Let simmer about 15 minutes. If the juice is not thick enough for your taste, mix a small amount of corn starch with cold water and stir in the hot mixture until thickened to suit you.