Coupons that have an expiration date will expire at midnight on the day you choose. So if you have a New Year's Day coupon that you want to be redeemable on January 1st, you'll want to set the date to January 2nd. That way right at midnight it will expire, giving customers the full day on January 1st to redeem.
Navigate to Marketing > Coupons and when you're adding a new coupon or editing an existing coupon, toggle the Limit the date range when customers can redeem this coupon. You'll be prompted to add a Redeem by date.