How to hang hard to hang picture
I would hang the frames on nails or screws with suitable heads, and then secure the frames at the bottom using double stick tape or poster putty. This will prevent them from being inadvertently lifted or bumped off the anchors.

I have found that drywall nails have the right combination of size and a wide thin head for this purpose. if you need to use hollow wall anchors, some drywall screws have a head with enough of a flange that they might work well.