I forgot one line. I had to convert to exponential form first and forgot to paste the line.. If you can try this. No warnings. V 10.02.

ClearAll[c1, c2, s, q];
eq = { v + c1*Sinh[c2] == 0 , v +  Sinh[-s*q + c2] == 0};
eq = TrigToExp[eq];
Reduce[eq, {c1, c2}, Reals]
Solve[eq, {c1, c2}, Reals]

You wrote the equations in Latex in one form, then in the Mathematica code you used different symbols. little confusing. Let me write your equations, and instead of using -v, just use v since it is the same. And used lowerCaseLetters. Since C is actually a Mathematica symbol. Not a good idea to use UpperCase first letter in Mathematica. So your equations are basically these

        eq = {v == c1*Sinh[c2], v == Sinh[-s q + c2]}

To use Reduce

       Reduce[eq, {c1, c2}, Reals]

And to obtain a solution with no warnings

       Solve[eq, {c1, c2}, Reals]