C# and Cocoa are totally different systems. You're unlikely to find a single solution which works in both.
Hunspell[
^] works on both Windows and Linux, but it has a very low-level API.
(It's actually built-in to Mac OS 10.6 and higher.)
There's
a .NET wrapper[
^] which is
quite easy to use[
^].
I've no idea how easy it will be to call Hunspell from Cocoa, though.