Using third-party repositories as recommended below is not supported by the Debian project and could break your system now or when you upgrade later. Use with caution at your own risk!
There are two ways you can install Seamonkey on Debian.
The first way is to acquire the 64-bit source tarball from seamonkey-project.org and install it following the instructions. This method can be problematic and does little to ensure that you will get proper updates on time.
The other way is far easier.
Edit your /etc/apt/sources.list file and add the following line to it: deb http://downloads.sourceforge.net/project/ubuntuzilla/mozilla/apt all main
Run sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 2667CA5C
Run sudo apt-get update
Run sudo apt-get install seamonkey-mozilla-build
The repository is maintained by nanotube on Sourceforge. Although it also has Firefox and Thunderbird in it, the package names are different from standard ones and so should not conflict with existing packages you have installed.