there have been occasional cases of ligers that weren't steral but it's rare. Just like with mules there is a rare non sterile one but then they have to brred to a tiger lion or a horse or mule since you wouldn't be able to find another nonsterile hybrid, most likely.

It only takes about 40yrs of intensive selective breeding to get a domesticated species it takes more if you aren't so strict in your breeding practices
http://en.wikipedia.org/wiki/Tame_Silver_Fox
http://www.freerepublic.com/focus/news/807641/posts

If you hybrid a domestic to a non-domestic it only take a few generations and after a certain number they aren't sterile any more, like with the small cat hybrids but with most of those it's usually just the male that's sterile as they are more closely related. And it's the same case as above they are non-domestic bred to domestic, then hybrid bred to domestic, hybrid to domestic till a generation that leaves them with all the desirable domestic traits but still looking like a non-domestic.

Mules haven't turned into their own species yet since no one has pushed to like they do with the hybrid cats but mules are still hugely popular.

If you think a Hybrid is wrong no matter if it's a hybrid breed dog or a hybrid exotic domestic species then there's nothing I can say but to those more open that might think a mule is okay but a liger isn't then it's worth thinking over a bit more.