Can I apply a second coat to my decking boards a week after the first coat? The area is full sun and the previous stain I used only lasted 2 years

Due to the amount of time that has past since your first coat applying a second coat may not be success. You can test this method by splashing a few drops of water on the surface, if the water soaks in you can proceed with an additional coat. If the water beads up the deck is sealed and cannot successfully take an additional coat of stain.