It really is how much time your plot requires.
If you want fast:
Consider that Coruscant-Corellia route is a major thoroughfare and has been mapped, traversed and gamed in every possible fashion over the last 2 dozen millennia. There's doubtless many shortcuts, cheat routes and quick hacks to save your trip some time, in addition to whatever normal accommodations the Core governments have made to that hyperspace lane to speed it up. Also consider that The Alliance(s) and The High Republic are not at war or in conflict in any way, so you wouldn't have slowdowns relating to military actions; equally these two factions are fairly stable and small, so they're able to keep a reasonable control over any potential piracy or problematic factors on the hyperlanes. You trip could be speedy and as fast as an afternoon jaunt with a good ship.
If you want slow:
Consider that the Coruscant-Corellia route would be massively popular, most everyone heads this way to get out of Coruscant. No doubt, everyone else knows about the same shortcuts and hacks that you do (lifehacker.holonet is a well-known site after all), and would be clogging up those as well as the main hyperlane. And while the Alliance(s) and High Republic aren't at war, they're still two separate governments you're traveling between, so you'd better have your passport and papers in order for the inevitable border checkpoint (no Schengen Zone here afaik). Patrolling law enforcement or nearby planetary security might slow down the lanes with routine stops or scans along the way, particularly at known jump points (remember that hyperspace journeys aren't just a straight line, but a series of hops). Finally, the hyperlane from Coruscant to Corellia is this long, curving loop around the Deep Core, since you can't just cut through, so it could add more time to travel around the "galactic beltway." Add in any slower speeds of hyperdrive, and you could take a few days to get to Corellia.
Pick your pleasure, or mix the two. Ignore what you don't want to adhere to, call it circumstances or sheer dumb luck (or maybe the Force is with you).