I believe the next coronation will remain (in essence) the same as it has for 900 years, but will have certain significant differences. Every coronation has had some differences - they just happen so infrquently that the average person doesn't notice! Of course, differences are going to be much more obvious now that there is television, internet, ceaseless media attention. (Side note - amazing when you think of it - the last coronation was the first one ever filmed! A reminder of how long HM has been on the throne!).
Remember that some parts of the ceremony occur due to law, others because of tradition, yet others are probably preferences.
First, I believe the next coronation will occur in Westminster Abby - led by the Archbishop as usual - unless the CoE is disestablished prior to the event. A British coronation isn't merely the installation of a head of state, but a religious ceremony in which the monarch is annointed.
Charles will be "Defender of THE Faith", regardless of what he would like, unless the British Parliament alters the title (it was created by Parliament in 1544), AND the commonwealth countries all agree (per the 1931 Statute of Westminster preamble).
I also think the Peers of the Realm will attend as before. Granted, most of them will be life peers rather than hereditary peers, but the House of Lords is still (in title) the Upper House of Parliament, and Peers are still the monarch's councellors. Hopefully, they wear their coronets and robes?
Now, there may be representatives of other faiths, and maybe a little less pomp and ceremony than in 1953, but the fundamentals of the coronation will likely remian the same as before.
What I think will be interesting is what William's coronation will look like. My guess is that Charles' coronation will cause people to really look at the elements of the ceremony in a modern context, and it will force the debate to begin. It will probably take too long to decide on major changes for Charles' ceremony, but will pave the way for major changes for William's.