Basically gessoed Masonite, correct? Do you live in a humid climate & is the back coated with gesso/primer too? Hardboard is fiberboard and those fibers swell with changes in humidity. If the back isn't coated, the painting will bend concavely.
I still have some fiberboard oil studies from art school in Baltimore (super humid place in the summer) and even after gluing 1" x 2" wood strips to the back edges, they'd come loose and continue to curl after a couple years. Even after re-glueing & using brads. Coating the back of the painting with gesso and/or primer helps a lot.
If you've got the back coated and the board isn't curling, you can get 20" metal or wood sectional frames from any craft store like Michaels, etc., put the kit together & slide the panel in, then brace the back edges with the supplied metal bendy strips. The kit also comes with hook/sliders that fit within the back tracks and allow you to attach wire, or have hanging mounts. These sectional frame kits are only for 2 sides, so you'll need two 20" kits.
In art school we'd make cheap wooden frames using 1/4" x 1.5 or 2" wood lattice, stained, painted, or just varnished or waxed. Butt-joined corners attached to the sides of wood canvas stretchers with panel nails, or to 1x2" wood braces on the backs of masonite paintings.
On an actual canvas with stretchers you can recess the first lattice strip slightly so that the outer strip appears to float around the canvas, for a more high-end art school frame job.