That is an excellent question! According to the endosymbiont hypothesis, that is exactly how modern plants originated; the chloroplast, once a free-living, photosynthetic moneran, was engulfed by a larger cell and was converted into an organelle. Many single-celled protists still exist which are rather animal-like, but have functional chloroplasts.
As you point out in your question, the recipient cell's natural protections would have to be suppressed in order for this to work. It has been discovered that, in cells with naturally occurring chloroplasts, a subset of the chloroplast and mitochondrial genes are actually found in the nucleus; it is suspected that this transfer is connected with the cell's acceptance of the endosymbiont's presence within the cytoplasm. It is possible that gene splicing to replicate this situation might be necessary to create a stable cell in your experiment.
Additionally, the recipient cell would need to be relatively unspecialized, having a thin cell membrane, no other pigments, and a large enough vacuole to supply the needs of photosynthesis without dehydrating the cell.