The practice of cursing and swearing at Imam Ali (a.s.) was officially introduced by Mu'awiyah.
It then became a custom for most of the Ummayad rulers, and continued for nearly 70 years. There are cases of some who refused to curse Imam Ali (a.s.), and they were severely punished.
Unfortunately, some Sunni scholars not only praise Mu'awiyah, but also refuse to accept this historical fact.
Of course, something that is worse than Mu'awiyah cursing Imam Ali (a.s.) was Mu'awiyah fighting against Imam Ali (a.s.) in the Battle of Siffin, and then usurping the khilafah from Imam Hasan (a.s.), and all the other atrocities he committed.
Here are some references from Sunni sources that mention Mu'awiyah cursing and/or commanding others to curse:
Sahih Muslim, vol. 7, p. 120, ch. merits of Ali.
Sunan Tirmidhi, vol. 5, p. 301.
Mustadrak 'ala al-Sahihayn, vol. 3, p. 109. [also see: vol. 1, p. 541].
Such things have also been mentioned in:
Musnad Ahmad, vol. 4, p. 369.
Tarikh al-Tabari, 124.
Tarikh al-Khulafa, 232.
Muruj al-Dhahab, vol. 3, p. 42.
The famous Sunni scholar al-Zamakhshari says that during the Ummayad era, seventy thousand pulpits were cursing Imam Ali (a.s.), introduced by Mu'awiyah. See; Rabi' al-Abrar.
Here is a link that has some of these narrations:
With prayers for your success.