I don't pressure them as I have never liked that being done to me. Anyone who comes in I offer a book and when they decline I tell them I will check back later after they have had a few more drinks. For the ones who say they can't sing, I advise them that if they pay attention, they will notice that it isn't exactly a prerequisite for karaoke. I try to make them laugh. For the most part, those who secretly want to try will eventually pair up with someone and do it--or their friend will invite them to join in on the chorus and they will yell along. That is when the cordless mics come in handy because you can hand them one. Then they get that post bungee jump adrenaline surge or applause addiction and they will progress from there.
The cordless mics also come in handy for those who's main obstacle is just not wanting to get up on stage. We have one really good but shy singer who insists on hiding around a corner when she sings. There are some who can be coaxed into a group song if rotation permits. Anyone ever notice that some of the most reluctant will hog the mic once the music starts?
For the most part, I am not too aggressive about it. If people are just made to feel welcome and comfortable then the transformation will usually take care of itself. For the most part it is their friends who will convince someone to finally get up there more than it will be me whom they would really rather prefer just go away. (Actually blackmail and threats often work, at least on teenagers who will never be the first one to sing--you find some friend to rat out that so and so wants to sing or knows a certain song and you throw the Taylor Swift at them and say who ratted them out and that you are going to make the rat sing, too, for being a rat, etc. Once you get one group up, then they all follow. But I have never tried this on adults..)
The ones I really like are the ones who say, "But I don't know all of the words." It doesn't matter how much you tell them that the words are on the screen--they are still paralyzed by the fear of forgetting them.
If the bar owner is willing, the sing a song for a free drink thing can work well. It gives people the excuse to say that they can't sing but they want the drink. Right now at one place, we are having a sing a song, get a drawing ticket thing going. The prize is 6 drink tokens which is worth singing for.