Purchase a ring guard (available at jewelry and department stores). These small, tubular inserts are clear and won't significantly alter the appearance of the ring. They fit over the bottom of the band and fill excess space between your finger and the ring.
Have a jeweler install a metal sizer on the inside of the ring. These small inserts are more discreet than plastic ring guards and may feel more secure.
In a pinch, make a DIY ring guard with clear packaging tape. Cut a 1/2-inch piece and roll it into a tight tube with the sticky side exposed. Fit the tube into the widest part of the ring band to fill the excess space. The tube sticks to both the ring and your finger for a secure fit.
Place a small, clear rubber band on your finger under the ring to keep the ring from sliding off. Orthodontic rubber bands work for very slim fingers, while clear hair elastics fit better over larger fingers.