Imām Sajjad (alayhi salam) taught us a number of different supplications. They are all found in The “As-Sahifa al-kamilah al-Sajjadiyya”, and also available at https://www.al-islam.org/sahifa-al-kamilah-sajjadiyya-imam-zain-ul-abide....  

Imām ’Ali (alayhi salam) recited the following dua when he was sick: 

In the name of Allah the Beneficent the Merciful.
O Allah! Whenever You bestow a bounty upon me, my thanks is always less and whenever You have tried me in calamities, my patience was always less.
Then O the one who never made my thanksgiving being low, and O the one who, when sent the calamities my patience was very less inspite of which
He never deprived me of anything and O He who sees me doing sins but never degraded me.
And O He who saw me openly committing sins but never punished me.
Send blessings on Mohammad and his progeny, and grant me cure from this sickness without a speck of doubt You have power over all things.

You may find his supplications at the “As-Safiha Alawiya” .