Garden Detective: grave-site plantings

Chrysanthemum 'Matchsticks' lend great fall color. Credit: Handout
Consider, too, the mature size of the plants. If the headstone is upright, you can use plants that grow up to about 1 1/2 feet tall; flat markers can be overwhelmed by large plants, so stick with low growers or ground covers. Finally, you probably want plants that provide interest all year long, or at least from spring through fall.
If you want to use only one plant that will provide multiple seasons of interest, Sedum 'Autumn Joy' would be an excellent choice. Thriving in full sun to part shade, it is drought-tolerant, perfectly sized at 12-23 inches tall and undergoes colorful changes throughout the season. Succulent foliage emerges in spring, and the plant puts forth flattened greenish flowers in summer that turn beige and gradually become tinged with pale pink hues that darken as the season progresses to rose, mauve and, by autumn, a seasonally appropriate maroon.
Or you might flank both sides of the stone with short evergreens, like dwarf spring-flowering azaleas, and fill the area between them with annuals such as New Guinea impatiens or Wave petunias for sunny spots, or vinca for sun to part shade. Both are available in a variety of colors. (Ordinary impatiens should be avoided, as they are susceptible to downy mildew.)
Another option would be planting a progression of plants to take over each season as their predecessors fade. This requires some maintenance, as you'll want to clear away faded plants as each season ends. You might plant a Chrysanthemum centered directly in front of the stone, with spring-flowering bulbs, like crocus, hyacinth and/or daffodils in a half circle directly in front of it. This way, the bulb plants will bloom before the Chrysanthemum emerges, and by the time their foliage yellows and is ready to be cut back, the mum should be getting ready to take over behind them. Plant summer-blooming daylilies on either side of the mums, and they'll provide color over the summer, when you can plant annuals where the bulb plants were. By the time the daylilies are done, the mum will be blooming. In fall, replace the annuals with pansies. They'll complement the mums until frost and return to fill in around the bulb plants in spring.
For flat markers, keep it simple with a ground-hugging evergreen, like blue rug juniper, planted between the grave and a half-circle bed of Sedum spurium 'Dragon's Blood' or 'Fulda Glow.'