Welp, going by the books, the rebuilding happened sometime between the end of Prince Caspian and Rilian's 20th birthday; and the appearance of Wimbleweather in Prince Caspian does tend to indicate that there were still some good Giants around at that point.
From a quick look at the text, there's no direct reference to what Cair Paravel was built of; the illustrations show stonework in the Western European style - but some of the brick castles in the Hanseatic area went up very quickly indeed; if I remember correctly, Malbork Castle (the gargantuan HQ of the Teutonic Knights) was a functional fortress within two years of its foundation.
In terms of construction, Cair Paravel is like a number of the Renaissence-era Loire castles; halfway between a fort and a palace (which fits with the early-Renaissence Telmarines) - have a look at places like Saumur or Château de Langeais; it's certainly feasible to speak of rebuilding one of those in a few years, especially with surviving solid foundations.
(Of course, this might be getting slightly too picky and precise, but hey...)
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From a quick look at the text, there's no direct reference to what Cair Paravel was built of; the illustrations show stonework in the Western European style - but some of the brick castles in the Hanseatic area went up very quickly indeed; if I remember correctly, Malbork Castle (the gargantuan HQ of the Teutonic Knights) was a functional fortress within two years of its foundation.
In terms of construction, Cair Paravel is like a number of the Renaissence-era Loire castles; halfway between a fort and a palace (which fits with the early-Renaissence Telmarines) - have a look at places like Saumur or Château de Langeais; it's certainly feasible to speak of rebuilding one of those in a few years, especially with surviving solid foundations.
(Of course, this might be getting slightly too picky and precise, but hey...)