If you’re on v9, the plugin ‘Axis Center’ came with the app on the Goodies disk. This plug was written by an inhouse Cinema guy and is essential. Otherwise you can find it at https://www.c4dplugs.com.
It centers object (or hierarchy) axes along any or all directions relative to points, edges, etc. I use it for precisely what you’re doing all the time.
Sounds like you’re coming from Maya because you used the word ‘translate’ when you could’ve said ‘move.’ In that case, if you’re bringing in models from other apps, you’ll also find that aligning an axis to a selected edge is a very useful feature in this plug.