Make cycling, fun, do some singletrack, encourage them to jump their bikes and go fast downhill. Taking your children 20 miles along a cycle track while you and the wife natter away together looking at the scenery is going to be slow and tedious for them, kids like adventure, ride to get somewhere interesting, follow unknown paths through woods to see where they go etc.
For me when I was a child I would be out on my BMX from sun up to sundown. We would build jumps from bricks and wooden planks off curbs onto landing ramps and try and jump it further and further each time. Or we would ride to the top of treacherous slopes and fly down them... the more excitement, danger and adventure you give them, the more interested they will be in it.
This has been my experience. Cycling has to have a purpose, be a means to an end, an adventure as SWJ says. Right from the beginning both mine were far more interested in tricks, stunts and messing about going to stunt parks and skills areas. Of course an interest in bikes came first and we've always used bike to do little things, all holidays invariably had some kind of bike involvement even if it was just buzzing around a campsite, riding to the beach or cycling out for dinner, so bikes went everywhere with us, which isn't always easy but once they become something that is just natural to get onto rather than a special effort, you've cracked it, the rest follows.
Right now, trail centres are the thing, I expect that will change in the future but what is so fantastic to see is just how natural it is to them.