Recently Macedonia signed a “good relations” treaty with Bulgaria, so Macedonia cannot be said to have bad relations with all of its neighboring countries; they get along OK with Kosovo too. Israel is another possible candidate, although it could be argued that de facto relations with Egypt are not so bad. How about Palestine? Qatar is a country surrounded by hostile powers, and for the time being they win this designation.
Belarus is on increasingly bad terms with Russia, but Russia has quite a few adjoining countries, and I am not sure if all of those relations are so bad. China has frosty relations with many neighbors, although with Russia you would call it mixed and “not yet negative.” And relations with “the Stans” are not terrible. They don’t like North Korea so much any more, even if they won’t topple it.
I think of Chile as bordering on a hostile Bolivia, but relations with Argentina are acceptable, even if Porteños look down on the Chileans for being provincial.
Then there are countries with only one neighbor, such as how Haiti and the Dominican Republic rather uncomfortably share the island of Hispaniola. Relations across Central America seem to have improved considerably.
Which countries are the other contenders for this honorary designation?