It seems that you have to combine the metro and bus. One method: take the subway Line 2 to Kecun Station and then transfer to Line 3 to the Zhujiang New Town Station. Out of the metro, you could take the airport shuttle of Line6 at the Zhujiang New Town Square to the airport directly.

Or, take subway Line 2 from Chigang to the Guangzhou Railway Station directly. The express airport shuttle of Line 1 could also lead you to the airport. But, this journey is longer.

Take Subway Line2 and get off at Yuxiu Gongyuan (Park), then find the Dongfang Binguan (hotel), there are airport buses there.