The colour of transition metal ions in aqueous solution is largely due to d-d transitions of electrons. This phenomenon occurs when the metal ion has an incomplete d-subshell ($d^1$ to $d^9$). Ions with empty ($d^0$) or fully filled ($d^{10}$) d-orbitals are typically colourless.

Let's analyze the electronic configurations:

1. $Sc^{3+}$ (Z=21): $[Ar] 3d^0$. Empty d-orbitals. Colourless.
2. $Ti^{3+}$ (Z=22): $[Ar] 3d^1$. One unpaired electron. Purple.
3. $Ni^{2+}$ (Z=28): $[Ar] 3d^8$. Two unpaired electrons. Green.
4. $Cu^{+}$ (Z=29): $[Ar] 3d^{10}$. Fully filled d-orbitals. Colourless.
5. $Co^{2+}$ (Z=27): $[Ar] 3d^7$. Three unpaired electrons. Pink.

Only the pair $Ni^{2+}, Ti^{3+}$ contains two ions that both have incompletely filled d-orbitals and exhibit colour in aqueous solution .