The end of apartheid in Zimbabwe comes to mind, but that's a pretty poor example considering how things turned out since

Japan and West Germany.

Ingredients for success:

• Leaving much of the bureaucracy intact
• The Soviet threat that pretty much forced the Germans and Japanese to cast their lot with the US
• I suppose the Marshall Plan helped too

The Korean War (1950-53)

This is not a perfect example -- it doesn't quite fit your conditions of "invasion" -- however it is similar enough in other respects as to be applicable, and so useful to your query.

The Korean War was a military intervention by outside powers, subsequent warring, resulting in the formation of new governments, one of which (South Korea) became a stable and successful democracy with a vibrant economy.

Possible reasons for the success of this example, as opposed to the countless negative examples, might be: the support of local populace in the war effort and the real desire on their part for outside assistance; the united nature of that populace, its cohesiveness and lack of major ethnic / religious / political divide (discounting North-South); the time period, not long after WWII, was one in which democracy was seen very much in a positive light, having been on the winning side of that global conflict.

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