The best solution is to install inner tubes. The tubes are available online, or at small engine repair shops. Liquid tire sealants are an easy solution. These liquid sealants do make a mess when you have to change the tire.
You can get a bead sealer from a quality tire shop or automechanic shop. It will probably work best and I would describe it as a liquid rubber that will seal the tires nicely. It is quick drying so no worries there.