What is Du'a to be recited for deceased woman and children in Janaazah prayer?

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. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Funeral prayer is performed with four Takbeer (Allaahu Akbar). After first Takbeer one recites chapter Al-Faatihah, after second Takbeer he reads Salat Ibraahimiyah (Allahumma Salli 'Ala Muhammdin wa 'Ala Aali… the one recited in Tashahhud during the prayers) and after third Takbeer he has to make supplications for the deceased.

If the deceased is male he should supplicate by these words:

"Allaahumma ighfir lahu warhamhu wa ‘aafihi wa'fu ‘anhu, wa akrim nuzulahu wa wassi’ madkhalahu waghsilhu bil-maa’ wath-thalji wal-barad, wa naqqihi minal-khataaya kama yunaqqath-thawb al-abyadhu min ad-danas. Allaahumma abdilhu daaran khayran min daarihi wa ahlan khayran min ahlihi. Allaahumma adkhilhu al-jannah wa a’ithhu min ‘adhaabil-qabri wa min ‘athaabin-naar." [Muslim]

(O Allaah, forgive him and have mercy on him, keep him safe and sound and pardon him, honor the place where he settles and make his entrance wide; wash him with water and snow and hail, and cleanse him of sin as a white garment is cleansed of dirt. O Allaah, give him a house better than his house and a wife better than his wife. O Allaah, admit him to Paradise and protect him from the torment of the grave and the torment of Hell-fire.)

If the deceased is a female then all the pronouns should be changed according to the gender. However, some scholars believe that it is not compulsory since the praying person means the dead person regardless of the gender. Imaam As-Syooti, may Allaah have His mercy on him, is of the opinion that one should avoid saying 'And husband better than her husband' since she might be for the same husband in the Paradise.

If the deceased is a child then the supplications should be made for his parents. The Prophet said: "A funeral prayer should be offered for an aborted baby, seeking for his parents the mercy and forgiveness of Allaah." [Abu Daawood]

It is desirable to say: "Allahummaj 'alhu lana salafan wa faratan wa Ajran" (O Allaah, make him a preceding reward, a prepayment and a recompense for us). [Al Baihaqi]

Finally, one pronounces the last fourth Takbeer and waits a moment and then finishes his prayer with one salutation towards his right side.

Allaah knows best.