There is no way to make a hen go broody. Some breeds rarely go broody, and some are more frequently broody, but you can't really do anything to make a hen become broody. It's kind of a hormonal thing for a hen, and you never know when it's going to happen.
A breed that I love, that is friendly, a great layer and has layed pretty long for me is actually a hybrid called the Golden Buff. I have only one left, and she is part of my original three first hens I ever owned. She's four now, and up until recently, layed a nice big brown egg nearly every day. The key in getting a friendly chicken is to really pay alot of attention to them when they're babies. And of course the breed helps too. I've had Easter Eggers, RIR, GLW, BR, Olive Eggers....They've all been friendly hens.
A GREAT hen to get to be a broody is the Silkie. They're mostly bantams, but they are the best broody hens. Cochins are good mama's too.