Does 青龙 not really mean Green Dragon?
青龙 should be translated as 'Azure (or Green/Blue) Dragon', that is the accepted translation for the mythological context. (Check some dictionaries, Pleco or CEDICT, they all use Azure Dragon, Wikipedia, and this Wiki article on the Four Symbols, too.)

Why would 青 mean nothing here? You can argue if it is blue, green or azure, but it is a color. Perhaps the people who translated 青龙白虎 as 'Dragon and White Tiger' just got confused about the different equivalents of 青 (blue, green, black) and left it out. 

If Wikipedia is not authoritative for you, you can try a site colon search on Google with site:edu 青龙 . This will search for 青龙 on the websites of American universities. You can see that most of these sources will give the translation as either Blue, Green or Azure Dragon. 

If you are still looking for some evidence, there are some books written on (or inspired by) Chinese mythology with the title bearing your expression: