You can cut your own out of bigger Mahogany, White Oak (not red), Teak or Ipe ONLY. An actual Lumber Store will have these and they will cut them for you...I'm not so sure about the drilling and countersinking though. Provide an or all of the old slats to them. Or, I only found them on Ebay-UK (
)...they aren't pre-drilled.
FYI, you may also have a Steel Support Strap in the middle, but on the backside. This piece is absolutely necessary and must be included in the renewed bench. It must be screwed into each and every slat for the bench to last or even work at all.
Finally, as you've now seen, you need to treat or protect the wood from weakening or other deterioration. For a small project like yours, I'd be tempted to go with polyurethane, but it doesn't last more than a few years and will have to be stripped every 10-years. I now only use One-Time Wood Protector (
), just slather it on every 7-years...indefinite shelf-life.