  A stable and high-quality single-magnon state is desired by the single-magnon
source for quantum information application with a macroscopic spin system. We
consider a hybrid system where a magnon mode is directly coupled to a
nonresonant superconducting qubit via the exchange interaction. The magnon and
qubit are under the driving and probing fields with the same frequency,
respectively. We find that the single-magnon probability $P_1$ can be maximized
when the product of the magnon-driving field detuning and the qubit-probing
field detuning is equivalent to the square of the magnon-qubit coupling
strength, $\Delta_q\Delta_m=J^2$. Then, the double-magnon probability $P_2$ can
be minimized by tuning the ratio of the probing intensity to the driving
intensity and the relative phase between the two fields. Under these optimized
conditions with accessible strong driving intensity and low decay rate, strong
magnon blockade gives rise to a stable single-magnon state with a high quality.
It features a large brightness (the single-magnon probability) $P_1\approx0.40$
and a high purity (the equal-time second-order correlation function)
$g^{(2)}(0)\sim10^{-5}$. The two indicators as a whole prevail over the
existing results for photon, phonon, and magnon modes with respect to a stable
single-quantum state. The optimized conditions with a scalable modification
$\Delta_q\Delta_m\approx NJ^2$ apply to the situation when one focus on only
one of the $N$ magnon modes that are simultaneously coupled to a common qubit.
