The first issue you need to deal with is where you say "the character amuses other characters, not the reader". As Lauren Ipsum points outpoints out, what you're basically saying here is that you're going to tell the reader the character's amusing, rather than show it. A character is believable because the reader finds him believable, not because the other characters find him believable, so you're already falling at the first hurdle if you can't make the reader see him as witty. This should be your top priority.
The other issue is the idea that the author must be witty or funny to make a witty or funny character. Not so. Must an author be a cold-blooded murderer or a withdrawn, melancholic cowboy to write those characters? Of course not, any more than an actor must be like the character they're trying to portray. What an author must be is a good observer of other people, and that's the best advice I can give you in order to write as another character. Observe friends, family or even strangers who are funny and witty, and see what makes them funny and witty. Read biographies of funny people. What made them tick? Get inside that person's head, and try to think like them. Not just how they're funny and witty, but why are they funny and witty. Do they do it to hide their own inadequacies? To divert attention? To become the centre of attention? There's an old saying: often a true word spoken in jest, so perhaps it's done to mask how they really feel in a funny way.
As a side note, it's not just telling jokes that makes someone funny. It could be puns or word play, it could be the ability to poke fun at other people or even themselves, or even just the way an ordinary story is told. Being funny and witty takes on many different forms, so don't just think in terms of "jokes".