When compared to other long standing empires like the Chinese and Persian empires civil wars seem to happen more often with the Romans.
No? It wasn't?
I don't know about the Chinese or Persian empires (though I will suggest the ascension of Darius was not really about making horses neigh), but Rome had a good 600-ish year run without civil war. Before Augustus, there was only civil war in a brief period of maybe 50 years between Sulla's first march on Rome in 88 BCE and the battle of Actium in 31 BCE. The next thing you might call a civil war came 100-ish years later in 69 CE.
After 69 we are getting out of my wheelhouse, and if you really want you'd have to find someone who can comment on Eastern Roman history down to 1453.
If we accept Rome's traditional foundation date of 753 BCE, we don't have any civil war until 88 BCE, and wars continue periodically until 31 BCE. Then a period of not-civil war until 69 CE. To me, that makes civil war look very much the exception rather than the rule.
If you're thinking about the later empire, you'll need someone else to help with that.