Ern, I have a small airbrush compressor like that, I used it for years, it carried the Badger name and works fine for small projects, mine still works after 25 years, that one looks like the ones sold at Harbor Freight if you have one in your area, they also sell online if you don't.
Here is a article to read about using compressed air tanks to compressors.
http://www.craigcentral.com/models/airsource.pdf
Compressed air tanks can be leased and we use them on the job for finish nail guns when it's a small job and don't want the sound of a compressor running. I lease three different sizes from about two feet tall to four feet tall, you pay deposit and the cost to fill.
Gary