"coincide precisely" is correct and can be used in written English.
You can use this phrase when two things exactly match each other, with no discrepancies. For example, "The dates of our holidays coincide precisely, so we can travel together."
The Deccan Traps eruptions, best seen in modern India, coincide precisely withe the K-T extinction.
The Siberian Traps eruptions, the largest of which we have a record, coincide precisely with the P-Tr extinction.
I'm willing to believe in faster-than-light travel; I'm not willing to believe that Hari Seldon can time his recorded appearance to coincide precisely with the latest crisis between Terminus and its neighbours.
But the event presented them with an opportunity to let loose in the company of peers, a rarity in a profession whose working hours coincide precisely with those during which most people like to go out.
He reiterated that France hoped for a speedy end to the conflict and voiced a plan for Iraq's future that happened to coincide precisely with that outlined by Mr. Blair today.
Why is it, therefore, that on many of the issues he cares most passionately about, Scalia's constitutional conclusions seem to coincide precisely with his personal preferences regarding affirmative action, school prayer, abortion, gay rights and gun rights?
The exact coincidence of the TSSs mapped by DMTSS and HTPS (56 TSSs) was 67%, while 64% of the previously mapped by other methodologies (121 TSSs) coincided precisely to the HTPS data, confirming the precision of our DMTSS methodology.
That change coincides precisely with the country's extraordinary economic surge.
The spore spike therefore coincides precisely with the iridium spike in time and is equally intense and short-lived.
Such criticism seems to have carried a particular sting for Maugham, perhaps because it coincided precisely with his own self-deprecating assessments.
The Saudi authorities perceived the Shia demonstrations as an assertion of Iranian policy, as they coincided precisely with Iran's celebration of the 30th anniversary of its Islamic Revolution.
