Look on the bottom of the chair. You should see where the cushions are attached, usually with screws or bolts. Remove the cushions and recover them by stapling new fabric over the old.
Are your cushions attached to the chairs with screws? You can unscrew the cushions and cover over top of the old with the fabric of your choice. Make sure you cut your fabric large enough to completely wrap over the cushion completely over the top and sides with an extra 3 inches to staple the fabric to the bottom of the cushion. Carefully pull the fabric taught (careful not to stretch) over the top, sides and underneath the cushions. Use a staple gun to attach the fabric to the underside of the cushion. Carefully pleat the excess fabric to fit and staple on top of the pleats. This process is SIMPLE! I've done my dining room chairs twice, my parents' kitchen and dining chairs twice and several desk chairs.
Here are some helpful Hometalk links.
How about upholstering the seats
it's so easy to reupholster a dining chair seat - here's how - https://www.charlestoncrafted.com/reupholster-seat/