Plasmonic nanostructures provide an efficient way to control and enhance the radiative properties of quantum emitters. Coupling these structures to single defects in two-dimensional materials provides a particularly promising material platform to study emitter-plasmon interactions because these emitters are not embedded in a surrounding dielectric. They can therefore approach a near-field plasmonic mode to nanoscale distances, potentially enabling strong light-matter interactions. However, this coupling requires precise alignment of the emitters to the plasmonic mode of the structures, which is particularly difficult to achieve in a site-controlled structure. We present a technique to generate quantum emitters in two-dimensional tungsten diselenide coupled to site-controlled plasmonic nanopillars. The plasmonic nanopillar induces strains in the two-dimensional material which generate quantum emitters near the high-field region of the plasmonic mode. The electric field of the nanopillar mode is nearly parallel to the two-dimensional material and is therefore in the correct orientation to couple to the emitters. We demonstrate both an enhanced spontaneous emission rate and increased brightness of emitters coupled to the nanopillars. This approach may enable bright site-controlled nonclassical light sources for applications in quantum communication and optical quantum computing.