I wanted to give a try to a recent version of rekonq (none in testing/unstable, the provided are more than one year old and buggy as hell), so I ended up on a rekonq package page on mentors.net. It provides a .dsc. To build the package, I did as follow:
dget -x http://mentors.debian.net/debian/pool/main/r/rekonq/rekonq_2.3.1-1.dsc cd rekonq-2.3.1 dpkg-checkbuilddeps dpkg-buildpackage -rfakeroot -us -uc
(obviously we assume that you have installed build dependancies as printed out by dpkg-checkbuilddeps)
Then to install it, it’s easy enough:
cd .. su dpkg -i rekonq_*.deb
On an related note, I have this problem with this version of rekonq that does not save my default search engine.