If you ever need to project an object onto the surface of another in Cinema 4D, you have a few options. Some methods for projecting geometry will work better than others, and even more nuanced, some methods are meant to work better on certain objects than others.
This tutorial shows a few methods to project a mesh on the surface of another mesh.
Here, CyBear, Lars Scholten, walks through some of the methods you can use for projecting geometry, one by one, and describes under which conditions each works best. Probably the simplest and most flexible is the Surface Deformer in C4D, Although you could use dynamic collisions, the shrink wrap deformer, or even spline projections, in a pinch.