I'd have my downline stick to doing their daily actions by logging in every day. That way, every ten or more VersaPoints they rack up per day will give them an opportunity to enter the Daily Grand contest.
For those who aren't strapped for cash, I'd also recommend setting up a Standing Order worth at least 1000 or more VP. They can grab the few hundred points needed to become (and stay) Executive Affiliate during the month just by completing the daily actions.