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. Here is a link to one company that sells small inexpensive floater frames. You might need spacers for them to sit properly.
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. Support a local business! If you can not do that or you are not finding what you like, take a look at some of these reliable mail-order frame sites for lots of options.
Below is a sample of the various floater frames you can order from the King of Frames site in California . If you assemble these yourself just glue the frame into the opening with either silicon (best because it is removable) 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.