It seems unlikely that they would refer to their enemies as the allies. Obviously, they will call them something in Japanese, German, and Italian, but what are those and what do they translate to?
There's a whole range of expressions even in Hitler's speeches. He often used simply unsere Feinde or die Gegner ("our enemies" or "the opponents"). Of course, when he got polemic, he started referring to the Allies as the "international plutocrat plot" or the "world jewry and its democratic helpers' helpers" - and later as "the jewish alliance between capitalism and bolshevism" once Russia joined the allies.
The german newspapers (all nazi-controlled, of course) had some choice words to describe Winston Churchill and the British during the early years of the war: Brits were Piraten during the war at sea in late 1939, and Churchill der Lügenlord (Lord of Lies).
Later, when british airstrikes over Germany became more frequent, the newspapers often referred to the British as die britischen Mörderer.
Source: William L. Shirer's This is Berlin: Reporting from Nazi Germany, 1938–40, a compilation of Shirer's daily live broadcasts from Berlin for CBS radio.
How did the Germans view the US?