Sorry but I have to post this, when I saw "How to deal with corruption??" this came to mind 
Alright, to stay on topic moving you capital to the 'middle' of your kingdom will help some. It costs 5000 like in SS. (as stated above
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Town Halls are good for corruption and in cities the barracks will help I believe. (cities only!)
Culture buildings boost happiness...
Taverns also boost happiness... But you're not having trouble with happiness though are you? Just corruption? This might make it worse then 
About the low tax thing Santana86 said, as Gondor I believe in order to survive you must use high and very high taxes unless it's changed since 2.1
(forgive me, I have not even played 3.1 yet, just modded it
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