Did any of the scholars permit women to use the tambourine (daf) on occasions other than Eids, weddings, and circumcisions?

None of the four schools of thought is devoid of an opinion permitting the [use of the] duff (tambourine) outside of 'Eid, weddings, and circumcisions. This is supported by the statements of scholars:

Hanafi School: Abu Yusuf's statement permitting a woman to play the duff for a child, provided there is no immorality. Maliki School: The counterpart to this is the well-known opinion permitting it for any Muslim celebration, such as the return of a traveler, 'Eid, circumcision, and the completion of Qur'an recitation. Shafi'i School: Imam [al-Haramayn al-Juwayni] and al-Ghazali held it to be absolutely permissible. Ibn Hajar al-Haytami stated that it is permissible without dislike in weddings and circumcisions, and permissible in other contexts according to the more correct view. He also stated that absolute permissibility is the ruling in al-Wasit and al-Wajiz. Hanbali School: The scholars of this school mentioned that it is disliked in contexts other than marriage. Some said [it is disliked] in circumcision, and others said [it is disliked] in other newly occurring joys.

Evidence for its permissibility is found in the hadith of Ibn 'Amr, where a woman vowed to play the duff in the presence of the Prophet, peace and blessings be upon him, and he said: "Fulfill your vow."