الجواب وباللہ التوفیق

To curse someone is to distance away from the blessings of Allah (SWT), while it is a secret order.

Therefore unless Shariat allows curse upon someone, no person has the right to precisely curse anyone. It is quite possible that the person being cursed upon may have repented and Allah (SWT) would have forgiven him.

However those persons who have been cursed upon by their specific names, like Pharoan, Qaroon, Abu Lahab etc. they can be openly cursed upon.

Also, people known for their bad character, can be cursed upon as; “cursed be the oppressors,  cursed be the transgressors”, without specifically calling them by names.

کما قال تعالیٰ: الا لعنۃ اللّٰہ علی الظلمین۔

 وقالؔ ومن یقتل مؤمنا متعمدا فجزاؤہ جھنم خالداً فیھا و غضب اللّٰہ علیہ ولعنہ واعد لہ عذاباً عظیما۔ الاٰیۃ ۔

Badmouthing someone is not allowed  and must therefore be avoided.

If there is a claim against someone, it is better to explore legitimate means to resolve the issue, rather denigrating someone.  

  عن عبد اﷲ بن عمرو أن النبي صلی اﷲ علیہ وسلم قال: أربع من کن فیہ کان منافقا خالصا ومن کانت

فیہ خصلۃ منہن کانت فیہ خصلۃ من النفاق حتی یدعہا إذا ائتمن خان وإذا حدث کذب وإذا عاہد غدر وإذا خاصم فجر۔ (صحیح البخاري، کتاب الإیمان، باب علامۃ المنافق، النسخۃ الہندیۃ ۱۰/۱، رقم:۳۴)

فقط واللہ اعلم بالصواب