All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
It is permissible to supplicate with other than the supplications that were mentioned in the Quran and the Sunnah if they do not include a religious prohibition. Abu Hurayrah narrated that the Prophet said to a man: “What do you say in the prayer?” The man answered: “I say the Tashahhud and then I ask Allaah for Paradise and I seek refuge with Him from Hell, but I do not understand what you and Mu'aath murmur (during the prayer). He said: ‘We murmur about the same thing.” [Ibn Maajah]
Some other Companions also narrated the same Hadeeth from the Prophet . [Abu Daawood and Ahmad - Al-Albaani and Al-Arna’oot graded it Saheeh (good)]
There is no doubt that the confirmed supplications from the Prophet are better and more beautiful and comprehensive.
Finally, it is not known that Al-Hasan Al-Basri authored books, but if such a book exists, then perhaps it is a compilation of some supplications which were related from him.
Allaah Knows best.