Just 系(けい) does the trick. (Learned this one from a friend with an ancestrally Mexican but American-born husband.)
E.g. メキシコ系, イギリス系, イタリア系
Now I'm not familiar with 日系, but the dictionary suggests it means an ancestral Japanese person who isn't a Japanese citizen. Is that incorrect?
My understanding of 中華 is that it means "Chinese food", so I wouldn't think that would be the right term to use, but maybe someone else can clarify. I think 中国系 should be good, though, following the same pattern as above.