I'd go for a BMX tire. Get a slick tire, if these paths aren't too rough. Knobs are only worthwhile for real offroad conditions. Otherwise they just slow you down and create noise on pavement.

Make sure to measure how much clearance you have for the new tire. How wide is the current tire? I'd say 35mm or so is plenty for gravel paths, if they're anything like the ones I'm thinking of.