Place Velcro strips on the chair and the cushion. Attach the Velcro hooks or "male" sides of the tape to the chair and apply the "female" sides or loops to the bottom of the cushion. Make sure the strips are placed so that they will match up when the cushion is placed on the chair. Press the cushion onto the chair to engage the Velcro strips.
Cut a piece of rubber shelf or drawer liner to the size of the cushion. Place the liner on the chair and set the cushion on top of it. The rubber liner will grip the surface of the chair and hold the cushion in place.
Attach cushions to the chairs using carpet tape. This vinyl tape is two-sided. Cut strips and apply them to the bottom of the chair in the outline of the cushion. Set the cushion over the tape and press down to adhere it to the surface of the chair. Carpet tape won't cause damage to the chair and will keep the cushions securely in place.