k,

Look into a small well and pump system close to your greenhouse. How far is a fair distance? Move the green house closer to your house. Rain catchment/barrel system or buy a big dog and fit him with water holding saddle bags. ALoha

Can't move greenhouse. I can't use barrels as we live in New Jersey and it does freeze here in the winter

k,

Do you heat the greenhouse? The dog thing is looking better and better. Aloha

Yes, I do heat the greenhouse in the winter. I discovered a product yesterday that maybe the answer to my question. The product is the Oasis Indoor Automatic Drip Watering System. It holds 6.6 gallons of water and runs on a 9 volt battery. Has anyone used this to date?

Kiropod, the Oasis is a good product, resevoir holds about 6 gallons of water. Here is another gravity fed system. Comes with the trays for your plants, there is a float in the tray that controls the water coming into it.
http://www.youtube.com/watch?v=xSnHZjXFRYU

Here is a link that might be useful: Grow Machine

That looks nice, but I have a raised bed garden in the greenhouse and would not work for me. Thanks!