jmc

We are told that $AC=3CB$, so $AB=AC+CB=4CB$. Let $M$ be the midpoint of $\overline{AB}$. Then, we have $BM=\frac{AB}{2}$.

Since $AB=4CB$, we have $CB=\frac{AB}{4}=\frac{BM}{2}$. In other words, $C$ is the midpoint of $\overline{BM}$.

Since $M$ is the midpoint of $\overline{AB}$, we have $M=\left(\frac{-1+3}{2},\frac{0+8}{2}\right)=(1,4)$.

Similarly, since $C$ is the midpoint of $\overline{BM}$, we have $C=\left(\frac{3+1}{2},\frac{8+4}{2}\right)=\boxed{(2,6)}$.