Yes, I would like both of these if they played a larger role in some type of system. As in, if you have a coronation you are considered more legitimate by your vassals and the commons. So if you took over a new kingdom, you might need to convince the priestly folks - through bribes or political favors - to support your coronation or else risk revolts and factional intrigues by your new disgruntled vassals. Not simply as an opinion modifier.
For public executions, I'd be interested if they played a part in some kind of justice system. Possibly where certain crimes warrant different responses. If I am a male adulterer, my crime might earn me a whipping (a sub-menu of torture?) or some other corporal punishment. My female counterpart in adultery might simply get death. Now, if I had seduced my liege's wife, my punishment under the law might still be only corporal punishment but he is quite wrathful and decides to have a public execution for me. This is beyond what the law calls for and earns him tyranny (or some other negative justice modifier) although perhaps not as much as he might otherwise since most people don't like adulterers very much and think I had this punishment coming. On the other hand, a rebelling vassal's public execution might net me a good chunk of justice with both the commoners and a certain type of noble (using the new vassal stance system) but would be offset by risking alienating the other vassals ("Nobles don't deserve to be executed like common criminals!") or the victim's family if they are powerful enough. In this way, public execution would be a tool to show that you are a fair and legitimate ruler but could not be used too frequently for fear of upsetting the political balance.
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