My tank can and has easily gone a day without power. a UPS is pretty cheap, $100 will have a 7 amp hour SLA battery. That's probably good for about 5 amps at 12 volts, 60 watt hours. Should keep an air pump running for 12+ hours. And you can wire them up to much larger batteries if you want.
The issue is though, they'll be a stepped sine wave output, not true sine. A lot of pumps don't work well on them. I don't know how air pumps handle it, but filter pumps in my experience rattle badly.
You might be able to find the cheapest true sine UPS and then wire it up to a handful more SLA batteries. That could keep you running for days, but the is going to cost a little more.
