Here are the most common reasons why many new coupons come out on the first of the month:
Many brands budget for a specific number of prints per month for a several month period. For example Pepsi may have budgeted 450,000 prints per month. Once the coupon hits 450,000 total prints, it has hit it's print limit for the month and will not show up. Now on the first day of the next month, the print number resets back to zero so that same coupon is likely to reappear again.
For Budget reasons, many coupon campaigns are based upon months. Say Heinz Mustard wants to run a coupon campaign, they will typically run it for a few months. They typically start the coupon(s) on the first of the month.
Usually about 50% of all new coupons will show up the first few days of the month.
Conversely many coupons tend to expire on the last day of the month. To maximize your savings, CouponSurfer recommends making a special effort to print coupons on both the first and last day of the month.