The colors are soft - but pretty.

Not all quilts have to POP POP POP!!!!

Calm and soothing is also good.

I agree with sashing... and a medium green, with perhaps blue cornerstones... they truly are pretty blocks...

I would take a block to the fabric store and hold it in front of myself and let it pick the color from a wall of bolts! I have very good luck in doing that sometimes. I think I'd lean toward the coral color, but a bit brighter than what is in the center block's flowers.

I would keep that quilt is soft, comforting colors - soft peach or very soft green - match the colors in the blocks with blenders.

The triple sashing with nine patch cornerstones quilt which was posted is gorgeous! That would look great with your blocks in soft (very light and a bit darker) colors.

I think a green pulled from any of the flower leaves or stems. And I might go with a solid, or something that reads solid. I do think a peach or pink cornerstone would be lovely.

If you use a darker color, the blocks will pop. G

I agree with HelenS. I did this recently with a baby quilt I was making. I couldn't find anything in my stash to make a sashing strip. I finally took the whole quilt top shopping and let it choose one. And I came up with a winner.

Peachy pink and a medium green pulled from the picture. I wouldn't use blue

You could even just sew the blocks together as is & then put maybe two framing boarders around them. The first one a thin border & the second much wider.