Uranus and Neptune have long been thought to harbour gemstones. But Saturn and Jupiter were not thought to have suitable atmospheres.
Baines and Delitsky analysed the latest temperature and pressure predictions for the planets' interiors, as well as new data on how carbon behaves in different conditions.
They concluded that stable crystals of diamond will "hail down over a huge region" of Saturn in particular.
"It all begins in the upper atmosphere, in the thunderstorm alleys, where lightning turns methane into soot," said Baines.
"As the soot falls, the pressure on it increases. And after about 1,000 miles it turns to graphite - the sheet-like form of carbon you find in pencils."
By a depth of 6,000km, these chunks of falling graphite toughen into diamonds - strong and unreactive.
These continue to fall for another 30,000km - "about two-and-a-half Earth-spans" says Baines.
"Once you get down to those extreme depths, the pressure and temperature is so hellish, there's no way the diamonds could remain solid.
"It's very uncertain what happens to carbon down there."
One possibility is that a "sea" of liquid carbon could form.
"Diamonds aren't forever on Saturn and Jupiter. But they are on Uranus and Neptune, which are colder at their cores," says Baines.
"Baines and Delitsky considered the data for pure carbon, instead of a carbon-hydrogen-helium mixture," she explained.
"We cannot exclude the proposed scenario (diamond rain on Saturn and Jupiter) but we simply have no data on mixtures in the planets. So we do not know if diamond formation occurs at all."
Meanwhile, an exoplanet that was believed to consist largely of diamond may not be so precious after all, according to new research.
The so-called "diamond planet" 55 Cancri e orbits a star 40 light-years from our Solar System.
A study in 2010 suggested it was a rocky world with a surface of graphite surrounding a thick layer of diamond, instead of water and granite like Earth.
But new research, external to be published in the Astrophysical Journal, calls this conclusion in question, making it unlikely any space probe sent to sample the planet's innards would dig up anything sparkling.
Carbon, the element diamonds are made of, now appears to be less abundant in relation to oxygen in the planet's host star - and by extension, perhaps the planet.
"Based on what we know at this point, 55 Cancri e is more of a 'diamond in the rough'," said author Johanna Teske, of the University of Arizona.