We required it.
Our daughter had a list of things to do every day (making her bed, brushing her teeth, setting the table, etc.) and we had "Read your Bible" on the list. At first she couldn't really read much, but it was a picture Bible and she enjoyed looking at it. When she got a little older we picked up one of those 'first reader' Bibles for her and she read that every day.
We didn't do allowances, so she wasn't actually paid for it, but she was praised/encouraged for doing everything on the list without reminders and there were consequences when she didn't do everything on her list. She never balked and I've never had any regrets. She outgrew the list on the fridge by the time she was 8 or 9, but continued to read her Bible each morning. She's 16 now and reading her Bible is as much a habit as making her bed and brushing her teeth is.
We require church attendance and participation in our family devotions, too. It's never been an issue - it's just what we do.
We've not had to deal with any resentment/rebellion over this, perhaps I'd feel differently if we'd had that struggle.