At first the time that was allowed for playing and singing was not long. - Здесь глагол-сказуемое is - непереходный глагол и страдательного залога не имеет.
В подчинённом предложении That was allowed for playing and singing. можно это сделать:
That is allowed for playing and singing.
That will be allowed for playing and singing.
That would be allowed for playing and singing.
That is being allowed for playing and singing.
That was being allowed for playing and singing.singing.