This is what you need
1 4'x4' peg board (about $13)

2 2"x4"x96" ($2.12 a piece)
plastic sheeting (we used durable plastic leaf bags)
2 bags of potting soil ($2 a bag)
2 rolls of sod ($5 a roll)
Here is what you do.
Lay the peg board down on the deck and cover it with the plastic sheeting or bags. Staple gun it or secure it under the peg board so the sheeting doesn't slip. Create a trim around the board using the 2x4's and secure in place. Empty the two bags of potting soil on top of the plastic cover peg board.
Roll the 2 strips of sod down. You will have a little extra that you will need to cut off.
Since Jack is a boy dog we bought a little plant for him to aim at to ensure he will pee on the grass. We also bought a hose attachment for our sink so we can spray off the grass and water it daily to make sure it doesn't die.