I'm Australian but my parents are Chinese so I had the same problem trying to find English teaching jobs in China. I'm in my mid-20's, have a university degree and essentially no teaching experience.
After applying to directly to several schools I registered with Gold Star TEFL Recruitment which is a free recruiting agency. They're really professional, replied to me the next day and I received several emails of interest from schools in China that same week. English First is a major chain school in China and the Taizhou branch didn't care about my ethnicity. Unfortunately I've heard some bad things about EF in general so I chose to work at York School of Foreign Languages in Fuzhou which is a small growing school who have just opened up their second branch in Fuzhou. I'm really loving it here: all the staff are great, we have teaching assistants, plenty of support and get to plan our own lessons. When I was applying I found that non-Chinese recruitment managers are more likely to give you a chance.
Hope this helps