Found it! In Good-Bye, Twilight, a collection of ballads compiled by Leslie H Daiken, published in 1936 with illustrations by Harry Kernoff, it's titled "Lines Written by a Republican Soldier in 1923", and is credited to James Ryan. It doesn't have the lines about Rory and Liam and Dick and Joe. Here it is:

Lines Written by a Republican Soldier in 1923

Take it down from the mast, Irish traitors,
'Tis the flag we Republicans claim.
It can never be owned by Free Staters
Who shed nothing upon it but shame.
Then leave it to those who are willing,
To uphold it in war or in peace,
Those men who intend to do killing
Until England's tyranny cease.

Take it down from the mast to remember
Your comrades who fell in the fight,
Those brave men who'd never surrender
To John Bull, that big tyrant of might.
The flag which to these men spelt freedom
From a foe that is centuries old;
Looking back on the past we can see them
Defending the green, white and gold.

I saw it in all the bright glory
When first it was flung to the wind,
When of freedom they told us the story
That no other nation could find,
When of martyrs their blood often freed us
Till a traitor to England had sold
The land that now sorely doth need us
To fight for the green, white and gold.

Take it down for its cause you have scornèd
To make permanent o'er us the Crown
You who linked yourself up with the foemen
The tricolour then to pull down.
'Tis we and no other can claim it
For to-day joined as one we stand, bold,
To fight England combined with Free Staters
In defence of the green, white and gold.
JAMES RYAN

(By the way, anyone taken with the ethos might be interested to read Gene Sharpe's influential handbook on non-violent revolution, From Dictatorship to Democracy )