Two to four inches isn't much space, just a thought can you grow Sempervivums in your zone? These are so easy care I've got them growing in straight gravel, some beautiful colors to choose from, some of the Sedums are pretty colorful too.
Annette

I wonder if beach heather would grow for you, sorry I don't know the proper mame, M

Dune plants are nourished by flotsam and sea spray.

You could try others, but you'll have to supply the nutrients.

Libby

Tiny Rubies dianthus (2") and Sedum acre (3") might fit in such a tiny space without looking 'weedy' and bending away from the house toward the sun. As Libby pointed out, you'll have to supply nutrients, including trace nutrients, that sand does not have.

My garden guru, Miss Billie, grows Sedum acre in coral rock from south Florida, so it is pretty tough. Sedum acre is growing in the crack between an asphalt drive and a brick planter here. It might survive with nutrients from dust off the patio. Dianthus might be a bit more demanding.

Nell

Along with the sedums and sempervivums (hens and chicks) you could try mother of thousands. When I Googled it, the name of the first one I saw was Kalanchoe daigremontiana, Crassulaceae. I have a couple kinds, one with narrow leaves, and the other with wide leaves. The only thing with them is they make new plants from the leaves and drop them, and they all seem to thrive. They are not perennials in our zone, though. I take some inside for the winter.

While I don't grow them in sand, last year, we put several pots of cacti and one of these in sand in a planter, and they dropped plants into the sand, and they grew.

Sue

Here's a pic of Sedum spathulifolium 'Capa Blanca' and I think Sempervivum 'Giuseppi' in a gravel path along side my greenhouse. The only soil is what came out of the pot with the plants. They're planted in straight driveway chip. Giuseppi turns a nice reddish color in the summer. Some Semps are even redder.

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You can get some nice texture and contrast in color just using these to easy to grow plants.

Annette

Annette's photo won me over. I'm thinking a combination of beach heather for height mixed with sempervivums. I always knew them as hens and chicks. I didn't realize there was such a variety. I have a few little sedums started in other gardens that I could transplant as well.

Thank you all for your ideas. I knew I could count on the creativity of this forum.

Squirrel girl

Squaw Mountain has a large variety of sedums and semps, will give some idea of how many different types there are to choose from. I'm thinking of ordering some myself in the spring to fill in around the steppers in a gravel path. Just thought I'd throw this teaser in :o).
Annette

Here is a link that might be useful: Squaw Mountain