While the Compton effect and the photoelectric effect are often used as "evidence" of photons, they actually cannot rule out completely the wave picture. The more definitive experiment would be the which-way experiment or the coincidence experiment. I find it rather amazing that such experiments are now within the realm of an undergraduate laboratory exercise.
There were 2 papers published in the American Journal of Physics that provided a very detailed description of such experiments suitable for such undergraduate laboratory. The first one is by J.J. Thorn et al. Here, they did the coincidence measurement that basically reproduced (with better equipment) an earlier Graingier et al. experiment. The second one by C.H. Holbrow et al. describes 5 different possible experiments (and theory to accompany them) to illustrate the photon pictures. No experimental result was reported in this paper.
Both papers contain a wealth of references, especially to other similar experiments that have already been done. That alone is worth keeping these two papers handy.