list of Chinese language country name abbreviations
I think this is a fairly exhaustive list of currently existing countries. This does not encompass unabbreviated country names that end with 国 (e.g., 孟加拉国):

Common


中国 (Zhōngguó) - P. R. China or R. O. China depending on context
法国 (Fǎguó) - France
德国 (Déguó) - Germany
泰国 (Tàiguó) - Thailand
英国 (Yīngguó) - England / UK
美国 (Měiguó) - USA
韩国 (Hánguó) - South Korea
俄国 (Éguó) - Russia
寮国 (Liáoguó) - Laos (chiefly Taiwan, the term is dated in mainland China. Use 老挝 (Lǎowō).)


Rare


奥国 (Àoguó) - Austria
葡国 (Púguó) - Portugal
墨国 (Mòguó) - Mexico
加国 (Jiāguó) - Canada