It's often hard to convince someone like this that they're wrong, because they simply don't want to believe they're wrong. Instead, they'll do everything they can to hold on to their position, no matter what you say -- or what God says in His Word.
Why is this? I don't know your brother-in-law, of course, but people who say this often are determined to be free to do anything they want to. In other words, if they can convince themselves there is no right or wrong, then they think they can live without worrying about God or His moral standards. Like the people of Ezekiel's day, "They have eyes to see but do not see and ears to hear but do not hear, for they are a rebellious people" (Ezekiel 12:2).
What can you do? First, help your brother-in-law to realize just how illogical his position is. If there is no right or wrong (as he claims), does this mean it's OK to murder, or abuse children, or steal, or persecute people we don't like? No, of course not. Down inside, we all know that some things are always wrong, even if we deny it.
But the most important thing you can do is to pray for him. Only God can convict him of his folly, and only God can convince him of his need for Christ. Right now, he's on the wrong road in life, but God loves him, and with Christ his life can be changed.