There have been codes for all different times of the year. Just depends on where you live and if you have an AP (annual pass). There have been Canadian discounts on occasion in the past.
Your best bet is to sign up with mousesavers dot com. They alert you as to when new codes become available. You can call WDW but they'll usually just tell you their "best" rate. If you have a code to give them then they can look it up. If you're looking for June, something may come available in March or April. Codes are usually released about 2 months or so out. It really depends on the availability of the resort rooms as to what's available for that specific time frame.
Also keep in mind there are different seasons such as, value, regular, peak and holiday so the discounts are less as the season is more popular (like peak). June is regular season, but it is still busy so it just depends on what's available after they sell at regular rates.