NO, no and no on astro turf!!!!Heavy hard to clean and stinks when dirty to high heaven when soiled. :B:B
A. Put up a contained kennel area for him - pea gravel
TSC has small outside portable chain link kennels on sale all the time.
OR
B. Put up an ex-pen and put down sun shade from Lowes underneath it and put stakes on all four corners.
I use the sun shade on the ground when RV'ing all the time under my ex-pens. You could put 2 expens together and it would be 'plenty' of room for your little guy to run around in and do his business.
I am an over the top dog person BUT your house and your lawn is YOUR domain and for YOU to enjoy not the dog!:C
The sunshade allows all water/pee to drain thru it AND the best part it allows you to pick up the poop cleanly with a scooper instead of smearing it all over when you try to pick it up on grass.
The sunshade is also real light weight an 8 x 8 piece of it that would fit under 2-expens will fit in a small bucket of soapy water to wash it in and hung up dries in 5 minutes. Or just squirt dawn on it in place and hose off, again dries quickly.
Good Luck!