Plants for grave sites is a common question that I receive. While it's probably a rural thing, I grew up helping my mom and dad maintain the graves of passed family members, recent and old. Over the years, I have seen what works and doesn't work for planting at the grave site.
Before planting anything, do take the time to check with the cemetery board or maintenance staff. They may have some guidelines about what can or cannot be planted. It is doubtful that they would want trees planted anywhere so the only tree selections here are for small growing varieties that will not spread much. Most plants are low growing perennials and ground cover plants that are not invasive.