Well the obvious candidate would be the Austrian Empire, they having such physicists as Einsteing, Fermi and the Oppenheimer brothers, but of course the Austrians had other priorities when it came to defence spending during the 30's.
Likewise the Russians were too cash strapped as was the CSA and the Japanese were wasting money and manpower trying to conquer China.
The only other countries capable of developing the Bomb were the ones that did develop it, Britain, the USA and the Empire of Brazil.
((does this work or would setting things in an ATL closer to OTL 1930's be better, i.e. having Hitler and his generals facing off against a nuclear armed France?))