Gift of the Magi was published in 1905. As others have already identified, the US had a two-cent piece until 1872 and a three-cent piece until 1889 (but with much lower production after 1875). The US does not demonetize coins: those coins are still legal for payment today (though I expect that they're worth a lot more than faith value to collectors). A total of 127 cents in non-pennies is possible if it involves two- or three-cent pieces in addition to perhaps higher-value coins.
Wikipedia, with citations of The Numismatist in 1909 and in 1954, indicates that about one third of the two-cent coins had been repurchased by the treasury by 1909, and that by 1954 “few alive could remember using a two-cent piece”. So in 1905, two-cent pieces would have been somewhat rare already, and this is likely true to some extent of three-cent pieces.
Now that we have the context, let's look at the text. This is the opening of the short story, so I expect the author was especially careful when writing it.
One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies. Pennies saved one and two at a time (…). Three times Della counted it. One dollar and eighty-seven cents.
We're told the amount twice. There's no room for errors or imprecision. There were definitely 60 pennies, not one more.
And apart from the pennies, some of the coins must be of a type that hasn't been minted in a couple of decades. This would have been apparent to a contemporary reader. Della has either been saving for a long time (perhaps not, since later the author tells us that “She had been saving every penny she could for months”), or she's trading with people who've been using small-value coins for a long time. She's not the kind of person who gets crisp notes from the bank.
The explicit and implicit information about the kind of coins Della has participates in making the reader understand that she's poor.