Food and Drink
Solicit cake donations from community members, then host a cakewalk. Charge entrants $1 per walk. Give it a twist by playing fast music and telling participants to keep the beat when they walk. Kids often enjoy a pie-throwing contest. Get a bakery to donate pies and ask local celebrities to volunteer some "face" time. Charge $1 per throw. You could also fill a jar full of candy pieces and charge $1 per guess of how many the jar contains or hold a hot-dog eating competition. Make the latter more lucrative by forming teams before the carnival and asking local businesses to sponsor them in exchange for advertising at the carnival.
Competitions
Hold a pairs' "decathlon" at your carnival made up of silly activities, such as a three-legged race. Divide pairs into age groups and charge $10 per pair. You could also set up a small stage with a backdrop, put a few chairs on it and host a variety of "game shows," such as The Newlywed Game. Charge each entrant a small fee. Host a general talent show and competition, or make it more specific, such as a freestyle competition or a dance-off.
Sports
Set up a goal post and hold a football throw, or hold a Frisbee- or baseball-throwing competition. Ask the local police department to bring a radar gun to measure each throw's speed. You could also hold a horseshoes or two-on-two basketball tournament. Set up a net and have a volleyball or badminton competition. Or, set up a soccer goal, recruit a local college goalie and charge entrants $1 to try and kick the ball past the goalie. Mini golf is often a hit with carnival-goers; if you don't have access to a full course, you can purchase a one-hole setup or create your own with boards and green felt.
Other Ideas
Host a petting zoo or set up a "hair salon" where attendees can get exotic spray-on hair colors. Create a "jail" area; find or construct a large cage, get a volunteer to be a "police officer" and tell attendees they can pay $1 to have anyone put in jail. The "prisoner" then must pay $1 to get out of jail. You could also dress up as an old gypsy woman and sell fortunes or set up a "wall of treasure." Cut five or six small doors into a large piece of plywood and place different objects (some prizes, some duds) behind them. Charge $1 to open a door to try and get a prize.