How about Marie Pavie? I was just reading about it on an old gardenweb thread of conversation. I was "googling" the same topic and found a conversation comparing White Pet rose to Marie Pavie rose. I found both of them online at Two Sisters Roses.

Take a look at 'Sunrise Sunset'. Its an Easy Elegance rose so should have real good disease resistance. Other EE roses that I've had for several years have shown excellent disease resistance & that is one of the traits they are trying to get in this series. I planted one this spring & was very healthy, vigorous looking & good flower production. It is putting out several nice long canes that hug the ground. I planted mine next to the street so I waiting to see how well it stands up to the snow, slush, road salt, etc. that will be plowed on it over the winter. HMF link to it below.

Here is a link that might be useful: Sunrise Sunset

Marie Pavie is not a ground cover rose. Look at The Fairy and its relations, ie Crystal Fairy, etc. Red Cascade is another, tho it is red. There are several new ones out, such as the easy elegance.

My local nursery has Drift roses on sale. The blooms are a nice shape and the foliage is good -- they might be a possibility for you.

I just saw my gardening friend's two Peach Drift roses, covered in blooms and doing well in spite of the lousy fall we've had so far. I've wanted this lovely rose for ages. It's a peachy pink so it might fit your color needs. Diane

I planted Ice Meidiland this year and it's growing like a weed. It grows very low to the ground with long canes. Covered in pearly pinkish white flowers, with dark, shiny, healthy foliage.

I did see the "Popcorn" Drift rose, soft yellow and cream colored in a rose catalog I received yesterday. The catalog was from Witherspoon Roses.

"Groundcover" is something of a cruel misnomer when it comes to roses. It seems that quite a few people who inquire about groundcover roses are looking for a variety that is ground-hugging, mat-forming, weed-suppressing. Unfortunately such a rose does not yet exist.

I grew white Meidland and it had black spot so bad, I pulled it out. A very pretty plant if it were healthy. Sorry.

I have the miniature rose Snow Carpet planted on top of a rock retaining wall, and was delighted to discover that it grows very mat-like, almost like a low sedum. It doesn't give me a lot of bloom but the foliage is lovely in the way it clings to the rocks.

You might consider "The Fairy", a beautiful, dainty, pink, modern shrub that can be ordered from the 2014 David Austin catalog, on page 73. I'd love to have some myself!