I am an American citizen living in China. I have taken in and raised two abandoned Chinese girls who I found as babies in the dumpster. How can I legally and safely adopt these two undocumented girls?

You made a mistake who didn't document them from the beginning. That is what you have to do now. If I were you I would contact a lawyer in China and ask what to do. I doubt these things happen often. It's illegal to dump babies in dumpsters in China and they should've known from the beginning and tried to find the real parents. Not reporting this was a crime in itself and you have 2 girls which you also should pay extra for if they were your own since there is more then one. You need to get a lawyer. Adopting them will not be the first issue you have to deal with I belevie. Not being documented in China means no school, no work, no health care.