You may want to look into DependeCo
http://dependeco-adult-diapers.com/. While they do have ABDL stuff, they also have a variety of solid colors and the usual white as well.
For nighttime, I use their white flannel pinned diaper inside the Velcro tabbed flannel diaper (thus, no need for pinning since the outer Velcro tabbed diaper holds everything in place); and a cover over that. And while bulky, I’ve never had a leak issue. Here’s where you can find the flannel items:
http://dependeco-adult-diapers.com/catalog.php?category=11.
Monika, the owner, is a gem. She will custom make anything you want at no extra charge. I wanted a diaper cover for daytime use. But I didn’t like the “high rise”. No problem for her; she made what I needed to the exact measurements. Even worked with me on options for achieving the lower rise I wanted. I just can’t say enough good things about her.