My kids wanted foam covered swords for sparring, and nothing on the market looked very good. So I made my own from swim noodles with wooden cores. And then the toddler wanted one, so I made her a smaller one, too.
Warning: These can give a good whack, so be careful to avoid injury to persons or property. Inspect periodically for damage to foam and replace foam in case of damage.
Buy a swim noodle. The narrower 2.5" diameter ones with 3/4" holes will make the sword less unwieldy. Consult kids on color. Ensure there are no rips and the holes are centered. I got mine at Academy Sports.
Get a wooden dowel. I went for poplar so it would have a bit of give and wouldn't be as heavy as oak. For durability, go for oak. You may consider rattan, which is what SCA uses.
You have a choice between 3/4" and 7/8". The advantage of 7/8" is that it will fit more snugly in the noodle. The disadvantage is that it will be 30% heavier, and even at 3/4" these swords are heavy enough that my 9- and 11-year-old like to use them two-handed. The 3/4" may rattle a bit in the foam (the hole in the foam tends to be a little more than 3/4") but the Gorilla glue should fill most of the gap.