Its supposed to be Earth, Vulcan, Andoria, Tellar and Alpha Centauri, with Mars joining within the next couple of years after the founding. Rigel is next, with joining dates varying (there are 5 different dates, though its worth noting that Rigel canonically has 12 planets, and in beta canon has 16 planets total, so its not like the entire system joins at once). But the entirely of the Rigel system is a member by the time Archer is President of the Federation.
I do not know if Denobula ever joined, considering Denobula’s stance on genetic engineering is wildly different from Earth, and the Federation as a whole. I know Denobula is still around in the 24th century, but that’s far different from joining.
I imagine that a number of Archer's first contacts joined between the founding and during Kirk's captaincy.
The Trill probably joined in the late 22nd century.
The Starfleet:Year One novel suggest Arbazans are a founding species. Note that Arbazans were only sen on DS9. That novel also suggests that the Vobilin are also founding members of the Federation
Starfleet: year One also notes that worlds of Dedderai, Dopterius and Osadj either are, or are under consideration, to join the Federation.
Terra Prime showed Andorians, Vulcans, Tellarites, Denobulans, Rigelians, Ktarians, and Coridanites.
Whether or not they all actually joined the UFP at the beginning is not clear, but a reasonable assumption, perhaps?
It just means they were willing to listen. Not that they were joining
The Star Trek: The Beginning screenplay had the Coalition of Planets members (circa 2159) as Earth, Vulcan, Andoria, Tellar, Rigel, and Denobula. So, going by the screenplay, some of them weren’t feeling the Coalition.
For some reason my head canon has Deltans as founding members but I don't remember why I think that
Deltans were known to space boomers. But beta canon suggests they didn’t attain warp drive in the early 2180s. Canoically, no one really knows what the history of the Deltans are.
It's somewhat unclear if Earth was alone in that conflict, or if it had significant support from its allies. The fact it's referred to as the Earth-Romulan War seems to suggest that Earth was mostly on its own.
I wonder about the circumstances behind that. What good is a Coalition of Planets if one of its founding members has to fight a war on its own?
There are plausible reasons none of them would participate.
Vulcan…T’Pau is a pacifist, an a leader of the Vulcan government. If she’s in charge of Vuclan for the majority of the war, that explains Vulcan’s lack of involvement. Its was noted that she got rid of most of the Vulcan fleet not long after taking over.
Rigel…in beta canon, its implied that they are less technologically advanced than Earth by the time the NX-01 is launched, despite being a spacefaring species for tens of thousands of years. So, they are out by default. Also, if Earth figures out that the Romulans are Vulcanoid, and draw conclusions with the Rigellians being Vuclanoid, Rigel might have been screened out of the war altogether.
Denobula…they might have a military, no one knows. All we know is that they were once at war with the Antarans, and that Denobulans are valued for medical and scientific reasons. Denobula might have turned their military a self defense force (like Japan's military) after their war with the Antarans and might not be of much help.
Andoria… Andorians seem very nationalist, and might have ignored Earth if it did not concern Andoria. The Andorian government is bigger than Shran and the Aenar, the latter of whom are pacifists. Plus, they might not think much of Earth after the Terra Prime incident, despite the work Archer and Shran put into building the relationship between their two worlds.
Tellarites…they were at odds with Coridan over trade with Orion Syndicate. Plus they argue a lot, and at some point, Earth probably wanted unity instead of any dissension, even though the Tellaraites are just practicing critical thinking loudly.
Coridan…in addition to trading with the Orion Syndicate, Coridan is a place of such importance in the Vulcan-Andorian conflict that Andorians for forbidden from stepping foot on the planet. And is a Vulcan puppet state, that's also in a civil war. Disregarding what happens to Coridan in the ENT novel
The Good That Men Do, they just might have been a political hot potato as is and was ignored. Even though they had the fastest ships in the quadrant.
