Is it permissible to supplicate for pregnancy and childbirth after a tubal ligation?

The default is that tying the fallopian tubes prevents pregnancy, unless there is a medical error. This can be verified with a hysterosalpingogram.

If the tube is open, pregnancy is possible, and one can supplicate for a righteous child. If it is closed, pregnancy is usually impossible, and supplication at that point would be an aggression (against divine decree). Daughters are a great blessing, and it is the blessing that Allah chose for His Prophet, peace be upon him. Allah Almighty says: ﴿To Allah belongs the dominion of the heavens and the earth; He creates what He wills. He bestows female [offspring] upon whom He wills, and bestows male [offspring] upon whom He wills. Or He couples them [as] males and females, and He renders whom He wills barren. Indeed, He is Knowing and Competent.﴾ And raising daughters carries a great reward. The Prophet, peace be upon him, said: "Whoever takes care of two girls until they reach maturity, he and I will come on the Day of Resurrection like this," and he joined his fingers.

If the closure of the two tubes has not been verified, it is permissible to supplicate for a righteous child, due to the possibility of pregnancy, however slight.