I tried to check the spelling, but I find there is no consensus. Gracenote lists
210 recordings with the spelling "Corina",
27 recordings with the spelling "Corine",
336 recordings with the spelling "Corinna",
128 recordings with the spelling "Corinne",
491 recordings with the spelling "Corrina",
283 recordings with the spelling "Corrine",
21 recordings with the spelling "Corrinna", and
24 recordings with the spelling "Corrinne".

AMG/All Music Guide lists
6 recordings with the spelling "Corina",
0 recordings with the spelling "Corine",
11 recordings with the spelling "Corinna",
0 recordings with the spelling "Corinne",
158 recordings with the spelling "Corrina",
162 recordings with the spelling "Corrine",
0 recordings with the spelling "Corrinna", and
0 recordings with the spelling "Corrinne".

So I guess the best we can do is list all those spellings and hope that anyone who searches for one of them finds this thread.