Preheat the oven to 325 F and lightly grease the doughnut pan.
Sift together the flour, sugar, baking powder, and salt in a large mixing bowl.
In a smaller bowl or measuring cup, whisk to break the eggs. Add the vanilla and canola oil. Add this to the flour mix, then pour over the Cheerwine. Carefully stir to mix everything together. Avoid over-mixing. You're looking to for everything to be just combined.
Spoon the batter into the baking pans. They'll rise a little, so don't fill each hole completely.
Bake until golden brown, about 10 to 12 minutes.
Remove from the oven and transfer pan to a wire rack to let cool for 5 minutes.
Tap the doughnut pan against the counter a few times, then flip it over to slide the doughnuts out. This goes faster than pulling them out by hand, and oftentimes ends up a bit prettier as well.