One that worked very well in NY was Sedum. It has succulent leaves and grows best with little water and does great in full sun. It blooms late summer and it thrives in the heat. It dies back in the autum and is not affected by the cold winter.

On our family plot, we planted a small selection of bulbs with staggered flowering times throughout the seasons. Over the last 30 or so years, not only have the bulbs well multiplied, but the collection has also grown thru family and friends who much prefer to add to the collection and pop in a bulb rather than leave flowers which only last a day or so. We've never had to water and it's the prettiest plot in the cemetery.

I so wish they would let me plant stuff on my mama's grave like that at the church! But they won't. I am trying to decide what to put in the urns on her headstone that would be green all year, and survive no matter the weather. any suggestions?

Kalanchoe, flower carpet roses, Mexican bush sage, dwarf bougainvillea and ornamental grasses all do well with neglect. Check your climate zone for frost hardiness.

Drought tolerance is increased by 25% or more, by adding 4 inches of wood chip mulch, which reduces evaporation and keeps the soil cooler, wood chips also supply all the fertilizing these roses will need, because they are closer to wild roses in their needs.
Yellow Lady Banks rose is drought tolerant to some degree, and with mulch should do well with little supplemental water in your climate, see if your garden is warm enough in winter for them to survive. There is also a double white form that is my favorite. These are climbing roses that need support, if you could put a 4' tall fence around the plot, that would suffice. Their foliage is quite ornamental. summer blooming only.
'Harisons' Yellow' is a tough hybrid of two yellow rose species, and it survived along the Oregon trail with little care. summer blooming only.
'Seafoam' is a pretty white rose, that was bred from the wild rose named R. bracteata, and it has very good rebloom, it grows to be c. 4' tall by nearly 6 feet wide, here. In the Earthkind trials in Texas, for roses, 'Seafoam' was found to be quite drought tolerant,(as was Belindas' Dream) both survived 2 months with no rain or supplemental water, in a hot Texas summer. These were established plants when the supplemental water was stopped.
Be sure these roses are grown on their own roots, and not budded or grafted onto rootstock.
For all these roses, I suggest you grow them at home in a pot, until their root systems are well established, which will take about a year, but the wait will be worth it.
Rose companion plants, that are drought tolerant in cool climates.
Parma violets. I bought mine from Canyon Ranch.com
these form very pretty clumps of heartshaped foliage with fragrant purple violets in spring. May need supplemental water 2-4 times a month, during the first year, if there is no rain.
"snow in summer' would be my first choice, as a rose companion, because it is more drought tolerant. Each plant will cover c. a square yard, and grow to be c. 4 inches tall. Dainty white flowers carpet it in summer.
Lavender, is another of my favorites for the drought tolerant garden, especially with pink and white roses.
Old fashioned Pinks, such as Little Gem from Canyon Ranch Nursery, the older pinks, are wild species,or close relatives of wild pinks, which receive little summer water in their natural environment. The same is true for some of the wild geranium species.
Luxrosa
p.s. Incidentally, I found an old garden rose, named "Grandmothers Hat' rosebush in an abandoned garden in Oakland, Ca, where the neighbors said it hadn't been watered in years, yet survived Oaklands' summer drought, which typically lasts from June through September. It's a gorgeous pink rose, and very fragrant, and reblooms. vintage gardens.com sells it own-root.
if there were room, this is how I would plant:
Parma violet-Grandmothers Hat- or Harisons Yellow P. violet
Pinks- 'Seafoam' -Pinks
snow-in-summmer, snow-in-summmer