I would use nonlinear least squares to fit an expression $C(t)+A(t) \cos \omega(t)$ with low degree polynomials $C,A,\omega$, trying different degrees for the different pieces and using BIC to decide on the best degree combination.
You may need to choose good starting values: Begin with $\omega(t)= a+bt$ with $a,b$ estimated from a Fourier transform. With $\omega(t)$ fixed you have a linear least squares problem for the coefficients of $C$ and $A$. Use the result with $\omega(t)= a+bt+0t^2+\ldots$ as a starting point for the nonlinear fit.
There seems to be a second high-frequency component in your data - inspect the residual to see whether this is noise or something significant. If the latter, add an additional term $+A_2(t) \cos \omega_2(t)$ and repeat. Here the starting point is chosen by working on the residual similarly as before.