Irony- “Great Nations of Europe” by Randy Newman

Ironic Examples:
"He [Columbus] shook hands with some Indians and soon they all were dead."
Shaking hands is a greeting and respectful tradition, it can sometimes represent truce. Columbus' shake meant  the opposite, murder to be exact. When first learning about Columbus and this gesture, the normal expectation is a friendly follow-up. However, you immediately realize the irony when learning that  the indians die. 

"He [Balboa] met some friendly Indians whom the Church told him were gay, so he had them torn apart by dogs on religious grounds they say the great nations of Europe were quite holy in their way."
Religious grounds are expected to be holy (saintly and moral) and that I know of, murder on religious grounds is disrespectful and plainly wrong. The song is mocking the nations' religious morality as well as the definition of holy by claiming that the nations were "holy in their way". 

"... the possibility that some bug from out of Africa might come for you and me
destroying everything in its path..."
Based on the great number of death caused by European brought diseases, it would be unexpected to have another disease via vectors affect the dominating and supposedly great nation. 

"The great nations of Europe comin through."
The song depicts continually the harm caused by these nations. There is nothing great about these nations exterminating different cultures.

Not Ironic Examples:
"Some bones hidden in a canyon some paintings in a cave
they're no use tryin to save them, there's nothin left to save."
The left overs as mentioned are only witness to the natives' existence. It is true nevertheless that they are useless because like I mentioned before they are only witness, not the real thing. It hits the realistic point  of their extermination directly.

"Now they're gone, they're gone, they're really gone. Yo never seen anyone so gone."
Like the previous example, it crudely states their wipe-out. By "really" they mean absolutely  gone and none are left. 

"Hide your wives and daughter; hide the groceries too."
This statement exemplifies the fear and magnitude created by the conquistadores' raiding of villages.  They were inhumane and it only seems logical to hide your loved ones from these monsters.