There are DNS services out there that can try to do this for you, they are not guaranteed to work though. The way they do it is by keeping the expire time on the zone low, and frequent checking of your server(s). If one goes down, they change the A record to point to the site that's up.
Another method you could try, although it's asking for trouble, is to use round robin DNS.. basically pointing to both your sites.. but you're at the mercy of the browser to make this work..
I recommend you simply find a host that doesn't really go down ever.. even if you pay significantly more to host your company's site at a reliable host.