Step 1: Define diamagnetism.
Diamagnetism is the property of materials that have no unpaired electrons. These materials are weakly repelled by a magnetic field.
Step 2: Check the electronic configuration of each ion.
- Cr$^{2+}$ and V$^{2+}$ both have unpaired electrons and are paramagnetic.
- Sc$^{3+}$ has no unpaired electrons and is diamagnetic.
- Ti$^{3+}$ also has unpaired electrons and is paramagnetic.
Step 3: Apply to the options.
Sc$^{3+}$ is the only ion without unpaired electrons, making it diamagnetic.
Final Answer:
\[
\boxed{\text{Sc}^{3+}}
\]