Well so far i can't give you an exact date etc. But according to tafsir ibn Kathir یوم الزینة was the day of festival:
That was the day of their celebration and their New Year's festivity.
It was a holiday for them when they took vacation from their work and
came together for a large gathering. This day was selected so that all
of the people could witness the power of Allah to do whatever He
wills. They would see the miracles of the prophets and the futility of
magic to contest the supernatural prophetic powers
In his tafsir Imam al Qurtubi summarized a number of possible meanings and interpretations for that special day:
- a day of festival in general people used to wear beautiful cloths at (according to Qatadah and as-Sudi)
- the day of 'ashura' (according to ibn 'Abbas (May Allah be pleased with both of them) and Said ibn Jubair)
- a day of market they used to wear beautiful cloths at (according Said ibn al-Mussayib and Qataddah)
- a Saturday (according to ad-Dahhaak)
- the day of Neyrouz or Nowruz ( according to a-Tha'alabi)
- a day the inlet of nil have been broken (water-level goes down-> end of flood) so it was a day people went out to look at the nil and feel safe from floods of the nil. In tafsir at-tahrir wa at-tanwir this is also described as a Coptic festival were some kind of embankments have been broken to let the water level of the nil go down!
But as the Arabic word الزینة refers to beauty or anything which is considered to beautify (For example it was translated mostly adornment in 7:32 see also the many Verses in surat al-Kahf, splendor in 10:88) and AFAIK there have been many celebrations and festivals in the ancient Egypt (see also here and in the Egyptian calendar in Wikipedia) according this the more probably festival could be the beautiful festival of the Valley or the beautiful feast of Opet which both would have been celebrated during the new kingdom period! An other possibility -which would go ahead with a lot of interpretations from tafsir books- would be the day of what was also known as the Coptic festival of the rivers which coincides with the day of beautiful festival of the Valley! As the Egyptian Neyrouz may have the same significance as the Persian/Kurdish Nowruz (New Year) but was hold around the September 11th there might have been some misunderstandings /misinterpretation as both would have been written the same way in Arabic letters!
And Allah knows best!