Wireless Time Machine Backup Without Time Capsule
You can still use a Time Capsule, just don't use it as a router. You can turn it's routing off by putting it in bridge mode (using the AirPort utility) and simply connecting a network cable between it and the existing router. You can turn wifi off as well if you don't want to use it, networking will happen via the existing wireless network.

As a somewhat cheaper yet officially supported alternative, an AirPort Express with an external USB drive works too. If the backups aren't too big, an older model works too, but since it's slower, big backups will take a while.

Alternatively, any NAS with "Time Machine Support" works out of the box as well, QNAP and Sinology make those for example.