Seeing as how China is written in Chinese as 中国, (zhongguo, IPA something like /tʂʊ̜ŋ gwɔ/), this means there is the potential for different transcriptions of the Western sounds /ʧaɪnə/ and /ʧi:nɑ/. The ‘proper’ Chinese characters mean ‘middle kingdom’. But there is plenty of scope to pick other characters to make the sound ‘Chai Na’ (or something similar), and give the name a more humorous or satirical connotation.
I posted about the use of 拆 before.
Now Language Log has provided a more expanded account of the wordplay (and the opportunity for cultural commentary within this) associated with transliteration, in the guise of a joke supposedly doing the rounds, based on how different people would render the sounds:
The playboy reads it as qiènǎ 妾哪 = where is my mistress?
The lover reads it as qīnnǎ 亲哪 = where is my darling?
The poor person reads it as qiánnǎ 钱哪 = where is my money?
The doctor reads it as qiènǎ 切哪 = where to cut?
The official reads it as quánnǎ 权哪 = where is my power?
The real estate developer reads it as quānnǎ 圈哪 = where can I encircle?
The dispossessed reads it as qiānnǎ 迁哪 = where should I move to?
The government reads it as chāinǎ 拆哪 = where should we demolish?