Yes of course there is a way to minimize the pain, people just want the liver to be some magical chi button. It's just flesh and nerves like the rest of your vulnerable bits, and nature has conveniently protected it for you.
Are you crunching your body to the side that the punch comes in on? That's the obvious step 1 if you aren't already doing that. Developing your obliques will help shield your organs. And finally you need to get used to getting hit there which helps with Frode's point. Do you think if you punched even the crappiest UFC fighter in the liver he would do anything other than laugh at you? No because they're used to getting hit there and can work through it. Medicine balls are one way, and having people kick or punch you there is another common drill. Give the striker a thumbs up or down depending on if they're hitting you too hard or soft so you don't have to slow down training by talking.
Edit: If you're talking really really powerful kicks, like a flush back kick, it can help to "roll" with the kick. Ride it across the ring rather than planting and eating 100% of the force.