The hadith appears in at-Tabarani's الطبراني encyclopedia's al-Mo'jam al-Awsat المعجم الأوسط -see here (in Arabic)- (longer version which is often -falsely. used as one of the evidences for performing adhan and iqamah in the ear of anew born they also show more than the prediction of the childs gender as it even quotes some further happenings of the offspring of this child and their names: as-Safah, al-Mahdi al-Mansur and that one of the latest will lead the prayer in presence of 'Isa) with the narrator chain:
an-No'maan ibn Ahmad النعمان بن أحمد (from)
-> Ahmad ibn Rushd ibn Khuthaym al-Hilali أحمد بن رشد بن خثيم الهلالي
-> (his uncle) Sa'id ibn Khuthaym سعيد بن خثيم
-> Handhalah ibn abi Sulayman حنظلة بن أبي سليمان
-> Tawoos طاوس
-> 'Abdullah ibn
'Abbas عبد الله بن عباس
-> Umm al-Fadl bint al-Harith أم الفضل بنت الحارث
and al-Mo'jam al-Kabir المعجم الكبير -see here (in Arabic)- via the narrator chain:
Al-Hussain ibn Muhammad al-Hannat ar-Ramuhurmuzi الحسين بن محمد الحناط الرامهرمزي
-> Ahamd ibn Rushd ibn Khuthaym al-Hilali أحمد بن رشد بن خيثم الهلالي
-> Handhalah ibn abi Sufyan (trustworthy) حنظلة بن أبي سفيان
-> Tawoos (trustworthy) طاوس
-> 'Abdullah ibn
'Abbas عبد الله بن عباس
-> Umm al-Fadl bint al-Harith أم الفضل بنت الحارث
Our first remark might be that basically the narrator chains have large overlap and it seems (assumption)that that of al-Mo'jam al-Kabir misses one narrator. Also one may ask whether the two Handhala's are the same person as:
In his al-Awsat at-Tabarni himself commented the hadith saying:
لم يرو هذا الحديث عن طاوس إلا حنظلة ، ولا عن حنظلة إلا سعيد بن خثيم ، تفرد به أحمد بن رشد .
In the following I'm translatiing from Arabic these translation is of my own take it with the necessary care!
None narrated this hadith from(via) Tawoos except with Handhalah nor from (via) Handhala except with Sa'id ibn Khutaym. Ahmad ibn Rushd was the only one narrating this.
In his commentary on al-Mawahib al-Laduniya sheikh Muhammad az-Zurqani (see here -in Arabic-)quoted the hadith part has been quoted by ibn Hebban and abu Nu'aym. And quoted himself the version of at-Tabarni from al-Mo'jam al-Kabir and qualified it as good (hassan). He also said that the versions of the hadith like that of imam at-Tabarni's al-Awsat ahve an issue, as neither adhan nor iqamah were known at the time.
Abu Bakr al-Haythami نور الدين علي بن أبي بكر الهيثمي quoted both versions of at-Tabarani in his Majma' az-Zawa'id مجمع الزاوئد ومنبع الفوائد. In his commentary on the version from al-Mo'jam al-Awsat -see here in Arabic- he commented on the narrtor "Ahmad ibn Rushd al-Hilali" who was accused due to this hadith. The fatwa #150966 from Islamqa considered it da'if jiddan (very weak) based on al-Haythami's statement.
Al-Hathami however agreed with the qualification on the version from al-Mo'jam al-Kabir -see here in Arabic- with az-Zurqani and said that the sanad is hassan.