If I was in your position, I'd probably use artificial grass for the patio. You can hose it off to clean it, it won't die, and it won't require all of the maintenance of real grass.

If you REALLY want grass:
Consider using a slightly raised (8") flower box.
Line it with a few inches of pea gravel, as it will help water drain away and keep the soil from trickling out of the cracks in the flower box. Fill the box the rest of the way with top soil and sod. Annual Rye Grass is pretty forgiving. You can set up the bed at a slight angle to drain the water where it will do the least harm. It must be able to drain somewhere or the roots will rot. If you go this route, you'll need to water and fertilize it regularly since there isn't enough soil to hold much water or store nutrients. You can use a grow light if you don't get quite enough sun. Given the less than ideal conditions, and small area, dog urine might kill off patches. Be careful with this approach if your patio is suspended (i.e. like a balcony) as wet soil can weigh a lot. This approach is best for a ground floor, and will require a fair amount of maintenance.

There is a product similar to the PottyPatch that you can buy in NY:
http://www.thepetloo.com/us/locate-a-retailer.html
I'd check it out in person and see if it would do the trick. I'm leery of buying an online pet product without ever having seen it, but this one you should be able to find in person. The big one on their main page looks pretty dog friendly.

Be careful with the PottyPatch. The consumerist has an article talking about how many people were unhappy with that company because of not receiving the product after ordering it:
http://consumerist.com/5306913/
Source(s):
http://www.thepetloo.com/
http://consumerist.com/5306913/

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