Step 1: Recall the definition of a conjugate base.
According to the Brønsted-Lowry concept, a conjugate base is formed when an acid donates a proton \((H^+)\).
Thus,
\[
\text{Conjugate Base}=\text{Acid}-H^+
\]
Step 2: Remove one proton from \(NH_4^+\).
The ammonium ion is
\[
NH_4^+
\]
When it loses one proton,
\[
NH_4^+ \rightarrow NH_3 + H^+
\]
Therefore, the species formed is
\[
NH_3
\]
Step 3: Verify the conjugate acid-base pair.
The pair is
\[
NH_4^+/NH_3
\]
where
\[
NH_4^+
\]
acts as the acid and
\[
NH_3
\]
acts as its conjugate base.
Step 4: Analyze the other options.
\[
NH^{2-}
\]
and
\[
NH_2^-
\]
are not obtained by removing only one proton from \(NH_4^+\).
\[
NH_4OH
\]
is ammonium hydroxide and is not the conjugate base of \(NH_4^+\).
Step 5: Final conclusion.
Hence, the conjugate base of
\[
NH_4^+
\]
is
\[
\boxed{NH_3}
\]
Therefore, the correct option is
\[
\boxed{(2)}
\]