Question

Do both black body radiation and the photoelectric effect support the particle model of light?

Answer 1

The phenomena of black body radiation doesn't care what form light is, wave or particle, but does care something about whether not the energy levels of light are discrete.

The photoelectric effect is ALL about the particle nature of light.

Answer 2

The above is true, but Black Body radiation is only mathematically feasible if light is considered in finite packets. So the answer to the question is yes, both of them support the particle model.