Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Ironic, Cynical
The idea that a young child could serve as a snack is just a tad ironic. The narrator "humbly" proposes his thoughts on cannibalism as if they're perfectly legitimate, ignoring the fact that they break every rule in the book (9). As readers, we know that eating children is not going to happen, no way, no how.
But by using an ironic tone, Swift gives us a glimpse at the terrible conditions in Ireland:
I can think of no one objection that will possibly be raised against this proposal, unless it be urged that the number of people will be thereby much lessened in the kingdom. (28)
Notice all that contempt? If Swift were Mr. Freeze, the slumlords of Ireland would be popsicles right about now. Swift's not shying away from harsh judgments of his least favorite landowners. But since he's writing satire, there's a little more leeway for rage.
The narrator may be perfectly sincere in proposing his solution, but do we detect a whiff of cynicism?:
For this kind of commodity will not bear exportation, the flesh being of too tender a consistence to admit a long continuance in salt, although perhaps I could name a country which would be glad to eat up our whole nation without it. (30)
Look out for moments when Swift is unable to maintain the Proposer's trademark jovial tone.