A partial and likely incomplete answer to this is the following:
fonts = FileNameTake /@
FileNames@
FileNameJoin[{$InstallationDirectory, "SystemFiles", "Fonts",
"TrueType", "*"}];
names = Union@Flatten[
StringCases[#, StartOfString ~~ Shortest[name__] ~~ "-" :> name] & /@
fonts
]
In the cloud this yields the following list:
{AlegreyaSC, ClearSans, Cousine, DroidSerif,
EBGaramond08, EBGaramond12, EBGaramondSC08, EBGaramondSC12,
Economica, Felipa, Inconsolata, Kalam,
Lato, LeagueGothic, Mathematica, MathematicaMono, MathematicaSans,
Oswald, PlayfairDisplay, Roboto, RobotoCondensed, RobotoSlab,
ShadowsIntoLightTwo, SourceCodePro, SourceSansPro, SourceSerifPro,
TitilliumWeb, VeraMono, YanoneKaffeesatz}
We can test these like so:
CloudEvaluate[Rasterize@Style["Font name: " <> #, FontFamily -> #]] & /@ names
This test reveals that Mathematica, MathematicaMono, and MathematicaSans cannot be used with general text. The rest seem to work.
Additionally, we can try these:
$FontFamilies
{Arial,Courier,Gill Sans,Helvetica,Source Sans Pro,Times New Roman,Trebuchet MS}
Of these, at least Arial, Helvetica and Trebuchet MS are not available. They fall back to the default font which looks different from any of these.
This is a naive function to try to test whether a certain font name is available (or rather: whether it renders differently from the default).
CloudEvaluate@Module[{rast},
rast =
Rasterize[
Style["Abcd Efgh Ijkl Opqr Stuv Wzyx ", FontFamily -> #,
FontSize -> 20], "Image"] &;
# -> (ImageData[rast["not a font"]] != ImageData[rast[#]])
] &