Karen, I think more "solid" butter would be better than a liquid oil. Depends, I guess
Are the directions specific regarding how to blend the sugar with the fats?
I've used oil successfully in coffee cakes (the Cafe Beaujalois one, specifically). That cake crumb is soft and tender.
But usually, shortening is "creamed" with sugar to break the crystals down and that creates a different basis than just mixing an oil with sugar.