I recommend floater frames for these small paintings. A floater frame lets the painting sit inside the frame without covering up any of the edges.
Also most of the 5 x 7 in. or 6 x 6 in. paintings have a slot on the back that allow them to be hung in a wall without a frame. And they can all be displayed on small easels.
Often a local frame shop can make a frame for about $50 ( or less) for a small painting. If you don’t want to do that and you are not finding what you like, take a look at some of these reliable mail order frame sites for lots of options.
King of Frame
Below I selected a few frames that I think look good. If you assemble these yourself just glue the frame into the opening with either silicon or any good strong glue. Don’t forget to choose the right dimensions for your frame. I don’t get any financial gain for these frames.