Q: What is a song that is about a government that can't be overthrown?

A:  I'll go one better than a song. Here's a national anthem.

Oh grand old Callahanastan,
Your fields are ripe with fruit.
Your women are so pretty.
Your clothes are so sweaty.
Your sports teams always win.

Oh grand old Callahanastan,
Where the work day starts at noon,
The weekend starts on Wednesday,
Moustaches are mandatory,
And Blu Rays are used as currency.

Oh grand old Callahanastan,
Founded so recently.
The people just decided
To surrender all power
After a bloody coup.


Oh grand old Callahanastan
Our loyalties run to you,
A benevolent ruler 
Of an exceptional land.
Please don't murder us

That's the anthem of a stable government. Whoever wrote that song, and their names have been lost to time but we can verify there were actual people, that the song was written by real people and not by the ruler of this country or a close associate, must have really loved the government. When you love something that much, the last thing you want is to see it end.

Fun fact about Callahanastan. The national anthem doubles as the constitution. You may find it weird that the constitution was written by a group of inspired citizens whose names have been lost to time, and not by any member of the government or the ruler himself, and ask why that is, but I would counter that by saying you have used your question for the day.