I search using ixquick.com because of their good privacy measures and they searh using post.

They have a button on their website that adds it to you list of search engines in chrome (chromium in my case), so it definitely can be done.

EDIT: it turns out that ixquick switches to a different URL and uses get instead of post for this, so forget what I said.

PS: the opera urlbar inline search has post support.