Is there any Islāmic basis to what is said that if a lady wears diamond, she will get ill?
There is, to our knowledge, no such narration recorded in the ḥadīth literature to support the above claim. In fact, since diamond is considered a jewellery, it will, InShāʾAllāh, fall into the following āyah, which permits the wearing of jewellery of all types:
وَهُوَ ٱلَّذِي سَخَّرَ ٱلۡبَحۡرَ لِتَأۡكُلُواْ مِنۡهُ لَحۡمٗا طَرِيّٗا وَتَسۡتَخۡرِجُواْ مِنۡهُ حِلۡيَةٗ تَلۡبَسُونَهَاۖ
“He is the One Who has subjugated the sea so that you may eat fresh meat from it, and may take out from it ornaments you wear.”
As for the false notion that she will fall ill, the ḥadīth literature is clear that there is no such thing as superstition in Islām. Imāms al-Bukhārī and Muslim ؒ narrate a ḥadīth in their Ṣaḥīḥayn on the authority of Abū Hurayrah ؓ, that Allāh’s Messenger ﷺ said:
«لا عدوى ولا طيرة»
“There is no such thing as a contagious disease, nor is there any such thing as a superstition.”
Therefore, we can conclude that the above is a false notion and a superstition; hence, it must neither be believed nor acted upon.
We surely attest that Allāh ﷻ knows best.
Answered by Shahin-ur Rahman, Bedford.
Monday 3rd Ṣafar 1437 AH / 16th November 2015 CE.
Checked and approved by Shaykh Dr. Abul Hasan Hussain Ahmed, London.
 [Al-Naḥl: 16/14]. A similar verse is in [Fāṭir: 35/12].
 Al-Bukhārī (5707) and Muslim (2220).