As usual, 26 January has been marked by protests, denunciations of those protests, and further iterations. Even apart from the fact that it marks an invasion, the foundation of a colony that later became one of Australia’s states isn’t much of a basis for a national day.
A logical choice would be the day our Federation came into force. Unfortunately for this idea, our Founders chose 1 Jan 1901. The first day of the 20th century[1] must have seemed like an auspicious choice for a new country, but it ruled out the anniversary as a national day.
The ideal thing would be to fix the problems of our current system with a republican constitution including a treaty with the original owners of our land. That would provide a date really worthy of celebration.
In the meantime, I suggest 3 March, the anniversary of the day in 1986 when the Australia Act came into force, finally establishing beyond any doubt that Australia is an independent country, entirely separate from the UK[2]. We had by 1986 a constitution and public policy that was at least formally non-racist, thanks to the 1967 referendum and the end of the White Australia policy. Many of the symbolic problems with the current date would be avoided, though the real injustices would remain to be addressed.
It’s true that the Australia Act doesn’t have a lot of resonance. But any date with a lot of resonance is bound to resonate badly for a large proportion of the population. At least this would be a choice nearly all of us could celebrate without worrying too much about its precise significance.
fn1. At least if you start the count from 1CE. I think it would be more sensible to cross-label 1BCE as 0 CE, making 1900 the start of C20. I had always assumed that Dionysius Exiguus, who invented the AD calendar was unaware of the concept of zero, but Wikipedia accords him a prominent role in its history.
fn2. Whether, when and to what extent, we had become an independent country before 1986 remains a mystery, but there’s no doubt after that.
John Quiggin 
This might be a repost as well, but the best day for a public holiday is the fourth Monday in January. It would mark the end of summer in much the same way Labour Day does in the US. There’s no need to call it anything other than the January Public Holiday, which is what they do in the UK with their bank holidays.
If it must have a name, how about Vaccination Day? Even Flag Day would be better than Australia Day.
I’m afraid I’ve never understood the point of Australia Day, but if we must have one, what better day than August 29?
In Affectionate Remembrance
of
ENGLISH CRICKET,
which died at the Oval
on
29 August 1882,
Deeply lamented by a large circle of sorrowing
friends and acquaintances
R.I.P.
N.B.—The body will be cremated and the
ashes taken to Australia.
As applicable today as when it was originally written and performed. Why do the First Peoples have to wait so long?
How about the first Saturday in January after the 1st January? All our elections are on a Saturday so we may as well use that as our mark.
Do we need an Australia Day at all? I would just rename 26 Jan as Indigenous Reconciliation Day, and instead of giving out Australia Day awards, I would give out awards to people who promote or exemplifies indigenous reconciliation.
In defence of Dionysus, he was probably thinking of calendar zero as a point, the singularity marking the Nativity. So AD1 was the first year after, BC1 the first year before. This plays merry hell with calendar arithmetic spanning the eras, but to an incarnationist theologian, that’s a feature not a bug.
You have nominated the birthday of my late father to be our national day. I have no objection, although from my point of view the birthday of my late mother would do equally well–that is, if it’s a good idea to have a national day at all, a point on which I remain doubtful.