There is Cotoneaster dammeri. Why must it be a shrub?

I suppose it doesn't have to be - any other ideas that might work well in combination with groundcover roses?

There are many factors to consider in matching a groundcover to the planting location. Can we see the space (and some surroundings)?

Our cotoneaster has sweet little white flowers followed by red berries. It also spreads rapidly.

Other conifers beside Juniper come in prostrate forms. How low do you want it to be?

Gaultheria procumbens grows in shade if you have acid soil.

Vinca minor (periwinkle) or cotoneaster, not quite a shrub but evergreen ground cover.

They grow well in zone 7 imho, I would rather use a native plant but do not know of any native evergreen groundcovers.

Gaultheria procumbens, mentioned above, is native to N E America.

So is bearberry or kinnikinnick, Arctostaphylos uva-ursi.

Thanks everyone for the suggestions! I will post a photo of the area once it is complete - it's basically the top of a slope set with some large boulders, so I want a combination that will give me some height variation but probably nothing over 2-3 feet tall. The slope below the boulders is planted with pachysandra, so it's possible that simply extending the pachysandra up into whatever shrubs I use is the way to go.

I have a dwarf red osier dogwood that's spreading, forming a very pretty mound. I imagine it will need cutting back eventually as it tip roots. It's about 2.5' tall and the top of a hill spilling downwards.

I have a mass planting of cotoneasters on a slope. I also have another slope that is planted with junipers. I have found that the junipers do a better job of weed suppression in case that is an issue for you.

My cotoneasters are not evergreen. Are there varieties that are evergreen?

Quite a few, actually. Although most, except for the low growing groundcover forms, tend to be only partially evergreen in colder climates or not very cold hardy at all and best in milder climates. And a fair number have rather invasive properties as well.

In the category of evergreen perennials, look at some of the evergreen Geraniums such Biokovo or Karmina or Veronica Georgia Blue, or some of the evergreen sedges.

I have found that Gaultheria procumbens is lovely as part of a groundcover community in at least part shade, but it doesn’t grow densely enough to be a weed suppressing ground cover on its own and it may burn in full sun in your area. I also wouldn’t recommend Vinca which is overly enthusiastic, rooting into the lawn and overrunning areas where I don’t want it.

Creeping Oregon Grape

https://www.monrovia.com/plant-catalog/plants/2479/creeping-oregon-grape/

Sun or shade?

Pachysandara (variegated, or maybe Greensheen) makes a fool-proof evergreen groundcover. You can use it as a filler and put larger shrubs in it.

Also Azalea 'Chinzan' is a fantastic spreading azalea. Can be kept to about 18" high and 3 feet wide if you like. Needs a bit of shade.