Brother, If the backup time is low, battery is the culprit, not the UPS. However what I use and suggest is a DC UPS for this purpose. Since router runs on DC, there is no DC-AC-DC inversion required through UPS inverter, hence less discharge for the same output. OK, now thats what you need to do.
- Get 12V-9Ah dry battery, will cost you around 1k max.
- Connect it to the same UPS you've got now.
- Take terminal out form Battery directly and plug those into your router.
- Enjoy the DIY satisfaction
Additionally:
1. Check polarity and rating on your router's adapter, It should be 12V (otherwise a little more circuitry is required).
2. Check battery charging voltage it shouldn't rise above 15V during charging, thats how much usual 12V electronics can bare. I'm using my wi-tribe wifi router at 14.5V, and its giving better coverage than its own adapter.
3. It should give you around 9 hours of backup if router is rated at 1A. If you need to extend this further, add another battery in parallel.