Is it permissible for an infertile person to supplicate with the noble verse: "My Lord, do not leave me alone [with no heir], while You are the best of inheritors" (Quran 21:89) to request offspring?

There is no harm in the aforementioned supplication. It is recommended to supplicate with "O Allah, grant me righteous offspring" or "O Allah, grant me pious offspring," as evinced by the noble verse: (My Lord, grant me from Yourself a good offspring. Indeed, You are the Hearer of supplication.) It is also advisable to consult doctors and to marry a fertile woman, for the Prophet, peace and blessings be upon him, said: (Marry the fertile, affectionate woman, for I shall outnumber the other nations through you on the Day of Resurrection.)