Where I am currently working, my predecessor, was not so diplomatic. This has made several business managers loathe to work with me, in fear that I would treat them the same way. My way of handling this is reminding them that I may be knowledgeable in my field of expertise (databases, technology, etc) but I am not an expert in all things (and I give examples of such: automobile mechanics, business law, etc.). I go further by stating that I do not have knowledge on how to do their job and am here to help make their job easier. I then circle around to the original reason why I am there (whatever the issue/problem is) and attempt to find out what is the root issue/problem. I then might suggest a few solutions and ask for their input (which is usually shocking to them since this is the first time something like that has happened). After they recover, it becomes a back-and-forth to create something they like verses whatever I choose to give them. I find this helps "win" over most people without having to resort to an "ego" driven approach.
I should also note: this does not always work since some individuals treat this approach as "weak". They become pretty surprised to find out that I can push back with the best of them (I made a few career-limiting-decisions in my early days at previous jobs in regards to pushing back forcibly - not something I recommend). I guess my approach is a like the iron hand/velvet glove. I want to get along with most people but don't mistake an easy-going approach for soft/weak.