Is it possible to have a stable Debian system, with the option to install single programs from testing/unstable with the distribution package manager?
A resposta é sim. Você pode usar os Backports da Debian.
Veja a página da web de backports
Diz
You are running Debian stable, because you prefer the Debian stable tree. It runs great, there is just one problem: the software is a little bit outdated compared to other distributions. This is where backports come in.
Backports are packages taken from the next Debian release (called "testing"), adjusted and recompiled for usage on Debian stable. Because the package is also present in the next Debian release, you can easily upgrade your stable+backports system once the next Debian release comes out. (In a few cases, usually for security updates, backports are also created from the Debian unstable distribution.)
Backports cannot be tested as extensively as Debian stable, and backports are provided on an as-is basis, with risk of incompatibilities with other components in Debian stable. Use with care!
It is therefore recommended to only select single backported packages that fit your needs, and not use all available backports.
Você pode precisar adicionar backports à sua lista de fontes. As Instruções do Debian Backports mostrará como