Praise be to Allaah.
There is nothing wrong with offering supplication like this, praying against the enemies of Allah and the enemies of His religion. It is narrated in the Sunnah that the Prophet (blessings and peace of Allah be upon him) offered this supplication against one of his enemies, namely the cousin of the Prophet (blessings and peace of Allah be upon him), the son of his uncle Abu Lahab.
It was narrated by al-Haakim (3984) and by al-Bayhaqi in al-Dalaa'il (622) that Lahab ibn Abi Lahab used to revile the Prophet (blessings and peace of Allah be upon him), and the Prophet (blessings and peace of Allah be upon him) said: O Allah, send Your dog against him. He went out with a caravan, heading towards Syria. He halted at some place and said: I am afraid of the prayer of Muhammad (blessings and peace of Allah be upon him). They said to him: No (don't worry). They surrounded him with their luggage and stood guard over him, then a lion came and snatched him and took him away.
Al-Haakim said: Its isnaad is saheeh. And al-Dhahabi agreed with him.
It was also narrated by Abu Naeem in al-Dalaa'il (220), where he mentioned his name as being Utbah ibn Abi Lahab, and in that report it says: O Allah, send against him one of Your dogs.
The hadeeth was classed as hasan by al-Haafiz Ibn Hajar in Fath al-Baari (4/39), al-Ayni in Umdat al-Qaari' (16/51), al-Shawkaani in Nayl al-Awtaar (5/80), and al-Sanaani in Subul al-Salaam (2195).
It should be noted that it may be appropriate to pray for destruction for a kaafir, or it may be more appropriate to pray that he be guided. That is according to the level of his hostility against the Muslims.
Shaykh Ibn Uthaymeen (may Allah have mercy on him) was asked:
Can one pray for death, destruction and punishment against the apostate or kaafir, or should we pray that he be guided? When should we pray for him and when should we pray against him?
If this apostate is harming the slaves of Allah and transgressing against their rights, then there is nothing wrong with praying against him and asking that he be destroyed, so as to ward off his evil. If that is not the case, then it is better to pray for him to be guided instead of praying against him to be destroyed. However, the duty of those who are in authority towards the apostates is to call them to Islam and to give them time, no more than three days. They have the choice of giving them this time, if they think that there is an interest to be served by delaying their execution. Then when the time is up, if the apostate insists on his apostasy, then he must be executed, because the Prophet (blessings and peace of Allah be upon him) said: Whoever changes his religion, execute him. End quote.
Fataawa Islamiyyah, 4/232.
And Allah knows best.