The phrase "amusing methods" is correct and usable in written English.
You can use it to describe techniques or approaches that are entertaining or humorous in nature.
Example: "The comedian shared some amusing methods for engaging the audience during his performances."
Alternatives: "entertaining techniques" or "funny approaches".
Sadiq Khan's EU-themed firework display on the London Eye was, mostly, an amusing method of winding up rightwing commentators.
Samantha uses an intriguing, and frankly amusing, method for determining how bold an albatross is.
Throughout the series, Gunther Steiner is highlighted for his harsh yet amusing method of managing the Haas team.
But Brearley had amusing, persuasive methods to galvanise others, such as on a hot afternoon promising the fearsome fast bowler Wayne Daniel an introduction to the attractive Tavern barmaid if he could summon up one more serious spell.
But some folks chose other, more amusing methods of protesting the agency.
Her pick, "Adhocism: A Case for Improvisation" (Doubleday) by Charles Jencks and Nathan Silver, is an amusing ode to a method of design that was as subversive as it was sustainable when the book was first published in the early 1970's.
On average, 80%% of users evaluated that the 20 Questions game is more amusing than the traditional method.
Another amusing and unconventional serving method is this one from caterer Pinch.
All office workers will have pondered how to ask for a raise but it took Georges Perec, in league with a computer programmer, to come up with a flowchart (later an amusing novella) on the precise method.
And while we might find their particular kind of contempt amusing, even hilarious, their intent and methods only differ from Ann Coulter and Rush Limbaugh with regards to politics, and that's not funny at all.
I find the water bath method much more reliable, if less amusing.
