In the new Disney canon, there are many dating systems, only two of which have been described:
Leland Chee, a creative executive with Lucasfilm, noted on Twitter in late 2016 that one such calendar, used exclusively by Rebels, is the ABY/BBY system from Legends, which takes the climax of A New Hope as year 0:
@c_gibbs1000: Does the BBY and ABY year designations apply in 'Canon' as it did in 'Legends'? Much appreciated.
@HolocronKeeper: It is one of many in-universe calendars. Out-of-universe, it makes more sense to use those years with the BSW4/ASW4 acronym.
@HolocronKeeper: As to who would use it in-universe, it wouldn't be any non-Rebel and it couldn't be used before BY.
He was asked the question again a few days later, and remarked that it wasn't a commonly-used system:
@JediSAS: Does/will official canon have a dating system the way Legends canon did (BBY/ABY)? [...] Crap, I forgot to specify that I'm wondering about an in-universe dating system. Oops.
@HolocronKeeper: ABY/BBY is one of many. Few would actually use and accept that one as standard.
The canon reference book Star Wars: Absolutely Everything You Need To Know reveals that the planet Lothal had its own calendar system. The only thing known about it is that the Empire was founded in 3258 LY:
This calendar is presumably based on the length of Lothal's orbit around its star; it's unknown how that relates to Coruscant's orbital period, so equating the two calendars is impossible.
It's unknown whether Lothal retained this calendar throughout its Imperial history.
In an episode of Rebels Recon, a behind-the-scenes show for Star Wars Rebels, Pablo Hidalgo revealed that planets synchronize their timekeeping with Coruscant:
Andi Gutierrez: Nolan Jiminez asks: "How is time measured in the galaxy if each planet has a different time of rotation and translation?
Hidalgo: We kind of assume that there is a standard hour, a standard day, a standard month; a unit of measurement that everyone understands how long that is; and, in our storytelling, we say that all that measurement comes from Coruscant. So, not only is it the galactic capital, it's sort of the yardstick through which all time is measured in the galaxy.
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Per the canon reference book Star Wars: Absolutely Everything You Need To Know, a standard day is 24 standard hours, and a standard year is 365 standard days:
It's unknown how, or if, this would have changed after the collapse of the Empire, when Coruscant ceased to be the capital of the galaxy; it seems unlikely that something like this would change, but you never know.