I think the most efficient way would be to take an edge loop or partial loop from the the sloping object and duplicate it. Then separate it(P) and scale/shrink it to where the center of your objects following the path should be. Next convert it to a curve and use a follow path constraint. If you want a detail explanation of follow path constraint then check out chapter 5: animate along a path 1 thru 4 in the Monster Truck Course. Lots of good advice to help you. If you want something more to the basics then check out: Pierrick Picaut https://www.youtube.com/watch?v=MXHW8nAURms
