Learn English – Single word to describe someone who is overly sensitive

A curmudgeon is someone who is bad-tempered and disagreeable - so curmudgeonly?

A contrarian is someone who takes an opposing view, especially for the sake of being difficult, contentious or in opposition to the generally held view. This could also be used as an adjective.

A troll is, in a certain context, someone who says something deliberately for the purpose of insulting or upsetting someone. (Thanks RegDwight AAA, and no offense intended to Norwegians).

My British friends and relatives might also say that such a person was "playing silly buggers" (or beggars).

Perhaps

pushover - a person who is easy to overcome or influence: Colonel Moore was benevolent but no pushover

or

patsy - a person who is easily taken advantage of, especially by being cheated or blamed for something

or

soft touch - (informal) a person easily persuaded or imposed on, esp to lend money

Of the three, the last is probably the most positive (at least in US usage). The other two suggest gullibility.