Having two vowel sounds doesn’t make it two sillables. Diptongs (sp?) are syllables with two vowel sounds; triptongs have three vowel sounds - but they’re still a single sillable.
Which brings me to the pronunciation of Siam as one or two sillables: if you stress the SI- so much it separates from the -am it’s two sillables, if you pronounce it all together (siam, not see-am) it’s one.
Eire read as if it was Spanish (which I’m sure is incorrect) has two sillables: EI-re
Not a straightforward question, because do things like “Democratic Republic of the Congo” (eleven syllables) count? Many countries have long, formal versions of their names, such as “Kingdom of the Netherlands” rather than the more familiar “Netherlands”. However, in the case of DR Congo some kind of long form is necessary to distinguish it from the other Congo.
I suppose we could ignore function words such as “the” and “of”, and non-unique words such as “republic” and “states”. In that case I think the winner might be Bosnia and Herzegovina (eight syllables not including the “and”).
And just to add that if we take the Anglicised official country name (according to Wikipedia), I reckon the winners are Federal Democratic Republic of Ethiopia (sixteen syllables) and Great Socialist People’s Libyan Arab Jamahiriya (arguably seventeen, depending on how you pronounce “socialist”).