I need to come up with a common time system but have no idea how to do it since I won't be able to go based on any one planet's rotation, or if I did it would inconsistent for most other planets.
You have no problem at all.
Greenwich Mean Time
As a point of reference, it's perfectly OK. There's no reason why everyone cannot constant reference the time from that point. OK, your species may not have Greenwich itself, but you can basically pick any arbitrary location as a reference and everyone else uses it.
Whatever time, day and date they say, you use as a base for your local system.
Your local system can apply it's own offsets ("timezones") any way it likes. It may have "local Greenwich Mean Time" which it's own planetary timezones reference, but which stays calibrated in some well defined way to the Main GMT.
You can pick any orbiting body or an artificial satellite for the Main GMT - this might be politically better, but it makes no difference to the system. I'd probably go with a system of reference satellites that can be tracked accurately and which can supply redundancy and self correction - orbital mechanics and perturbations from a variety of sources will need something like this.
Days and Dates are kept in broad sync (allowing for local, but well defined, offsets) by everyone following the Main GMT reference for date.
Precision timing will be done using atomic clocks. These can be used to keep a strict scientific watch on time as measured in each reference frame (relativity applies). But there's no need to use these for date and time directly. We'll have our Main GMT (and it's own clocks) and the Local GMTs which reference off the Main GMT so that relativistic effects don't get lost.
Now this isn't exactly trivial. There are lots of complex effects due to relativity, but there are scientists and computers for handling the details and they're pretty good at this, so leave them to it and don't argue.
How long is a Year, etc.
This is a political thing. There's no reason why local systems cannot operate (as custom) their own day, month and year stuff. But in practical terms for business, military and (really) staying sane, people will either work with the standard date or translate to it (aren't computers wonderful - no need to actually do the calculations yourself !).
If experience tells us anything it's that politically you solve the problem of different systems largely by working around it. Trying to ram a time system down one planet's throat that they don't want might well start a war, so diplomats just rename things and define abstract standards that people can "adopt". Computers will do the dirty work. You'll find suddenly that companies work to e.g. ISO-19288645 time and only some poor software developer has to actually understand the darn thing - everyone else just looks at their smart phone !
it would inconsistent for most other planets
Just to emphasize : you do not need consistency in terms of using the same system. You need systematically well defined local time systems that can be translated into each other (by computers) and kept track of using well defined reference points.
Because politics is involved (different races, different planets), they'll not actually agree an existing standard. To save face they'll invent a complete new one that is different from all the existing systems and no one likes for that reason. It will, over time, become an unavoidable standard everyone kind of knows or has to occasionally reference (e.g. in a business memo), but locally we'll all still use the system defined for local convenience.
So The Year of The Twelve Tailed Finch may be starting on Planet Mongo, but here on Planet Mango we're in the middle of the Imperial Year 27816. The ISO standard may say it's Dec 7th 1942, but no one cares about that.
Computers - stopping wars is our business.