I guess, there is some error in your first equation, where there should be $C_v$ instead of $C_p$.
For a reversible process:
$$dQ_{rev}=dU+dW$$
$$dQ_{rev}=nC_vdt+PdV$$
Dividing by $T$, and substituting $P$ from ideal gas equation $PV=nRT$
$$\frac{dQ_{rev}}{T}=nC_v\frac{dT}{T}+nR\frac{dV}{V}$$
Integrating from $T_1$ to $T_2$ and $V_1$ to $V_2$:
$$\Delta S_{sys}=nC_v\text{ln}\left(\frac{T_2}{T_1}\right)+nR\text{ln}\left(\frac{V_2}{V_1}\right)...(1)$$
Now $$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$
Now substituting for $\frac{V_2}{V_1}$, we get:
$$\Delta S_{sys}=nC_v\text{ln}\left(\frac{T_2}{T_1}\right)+nR\text{ln}\left(\frac{P_1}{P_2}\right)+nR\text{ln}\left(\frac{T_2}{T_1}\right)$$
From Meyer's Relation $C_p=C_v+R$, and simplifying above equation:
$$\Delta S_{sys}=nC_p\text{ln}\left(\frac{T_2}{T_1}\right)+nR\text{ln}\left(\frac{P_1}{P_2}\right)...(2)$$
From second and first equation you can find $\Delta S_{sys}$, for any kind of situation which is reversible.