"tirade of" is correct and usable in written English.
It is often used to refer to a long, angry speech or rant. For example, "The manager shouted a tirade of insults at the employees."
Could he perhaps emulate Harry Truman's successful tirade of 1948 against the "do-nothing Congress"?
You've got to be good-humoured to carry on this vast tirade of talking all day.
He calls to unleash a tirade of abuse – "This is your fault.
"Heather lunged at her and launched into a second tirade of abuse.
After a tirade of insults, Haughey dismissed him and returned to the work on his desk.
Two police vans turned up to take him away, ending the tirade of verbal abuse.
Like being stopped in the street and hit with a tirade of puerile, outdated incoherence.
Pumped with adrenaline from my sprint, I unleashed a tirade of epithets.
Alternately, he would go into a mournful tirade of apology and then throw up.
The tirade of Jimmy Porter is resumed in a different key by a frustrated solicitor in Osborne's Inadmissible Evidence (1964).
A tirade of ignorance about gay people, African-Americans, Muslims, Shintos and vast swaths of Eastern and Central Europe?
