Although made for Debian Etch and Ubuntu 6.10 (Edgy) the Zattoo 2.2.10.6523 build [1] works with Feisty Fawn. The following installs had to be executed:
$ sudo apt-get install libxul-common libmozjs0d libnspr4-0d libnss3-0d libxul0d
$ sudo dpkg -i zattoo-2.2.10.6523-i386.deb
[1] https://zattoo.com/downloadlinux