Step 1: Understand the colored ions.
Ions like Cu\(^{2+} \) exhibit a characteristic color due to d-d transitions in the metal ion. Fe\(^{2+} \) also shows color due to similar transitions, but Ti\(^{4+} \) and Co\(^{2+} \) do not exhibit color in their common oxidation states.
Step 2: Conclusion.
Thus, the group containing colored ions is Cu\(^{2+} \).
Final Answer:
\[
\boxed{\text{Cu}^{2+}}
\]