Let me play devil's advocate for a second. You want me to sit down and pay your bill once a week, right? I'm a busy person with a household to run, kids who need my attention, a job that's demanding, and lots more going on that takes every waking minute to keep up with. So I let your bill slide. And you come the next week even if I do, so what's the harm?
(I have been this person, for the record. Not because I don't rightly owe my lawn guy, but because making time once a week to do this was a PIA.)
So, what do to? You can send a reminder, which these customers are likely to ignore. You can stop coming until they're paid up, which means you'll lose them as customers unless you're the only game in town. Or you can make it way more convenient for them to pay you.
What I'd consider:
Biweekly billing, every other week.
Collecting in person, going to the houses in the early evening. (Eats your free time.)
Online payment, if you don't already have that set up.
Monthly billing, with the dates of the mowings indicated.
Prepayment for a month, no matter how many mowings it takes to keep up (and a discount for prepaying?).
Late fees for payments not received in a timely fashion (could cost you business)
Prepayment for the entire season, no matter how often you have to mow, and a bigger discount for it.