Don't use anything as a backer plate that will absorb water and/or rot - like a piece of wood.

Take a piece of fiberglass mat and wet it out with resin on a plastic sheet. After the resin has gone off, but while it's still "green" and somewhat flexible, trim it to size with scissors (about 2X the size of the hole), and lace a piece of fishing line through the middle. Gob some thickened resin on it, insert through the hole and pull back with the fishing line. Keep tension on the line until the resin sets.

The rest of Jake's advice is spot on.