"Unexcused absense" is so-called ”無断欠席” in Japanese, but I've actually never heard of antonym of ”無断欠席.” ”欠席届け” is a term often used in Japan to report the absence beforehand, so I would assume "excused absence" would be ”欠席届け済みの欠席.”

JP Google hit for ”無断欠席” is 16587, ”欠席届け”　is 1389.

Hope this helps!

These 2 terms may not correspond completely with those in English, so I will explain them here.
公欠 is not counted as absense, but they are granted only on limited occasions like:
1. You are representing school out of classes (sporting competition, etc).
2. You have a legally designated contagious disease and have to stay home or be hospitalized. This does not include common cold and the like.
3. You have appropriate reason to be absent from school (sitting for an entrance exam for higher schooling, being officially requested to attend a training session by a future employer, etc.) Whether a reason is appropriate or not is at the discretion of each school.
All other absences are regarded as 欠席 whether or not parents are aware and/or notify the school in writing. If the number of 欠席 exceeds a certain limit, often children cannot move up to the next grade or cannot receive credit for the subject.
忌引き (absence for a death in the family) is usually treated the same as 公欠 up to a certain number of days.