When we put down river rock in our gardens out front, we first put down black sheets of plastic. Five years later, weeds are plentiful. However this tip from Parent’s Room looks like it could work,
The newspaper will prevent any grass and weed seeds from germinating, but unlike fabric, it will decompose after about 18 months. By that time, any grass and weed seeds that were present in the soil on planting will be dead. It’s green, it’s cheaper than fabric, and when you decide to remove or redesign the bed later on, you will not have the headache you would with fabric.
My bet is you’ll have to re-do it in another year, though!