The Gamow-Teller (GT) strength distributions and isobaric analog resonance (IAR) states of several $N=Z+2$ nuclei with mass number $A=42--58$ are studied by using a self-consistent Skyrme Hartree-Fock-Bogoliubov method plus quasiparticle random phase approximation (HFB+QRPA) formalism. The isoscalar spin-triplet pairing interaction is included in QRPA on top of the isovector spin-singlet one in the HFB method. It is found that the isoscalar pairing correlations mix largely the $(\ensuremath{\nu}{j}_{>}\ensuremath{\rightarrow}\ensuremath{\pi}{j}_{<})$ configurations into the low-energy states, and this mixing plays an important role in the formation and in the collectivity of these low-energy states. Furthermore, the observed excitation energy of the low-energy GT state with respect to the IAR can be well reproduced when the strength of isoscalar pairing is about $1.0--1.05$ times that of the isovector pairing, irrespective of the adopted Skyrme interactions. In $N=Z+2$ nuclei in the middle of the $pf$-shell, a mutual cooperative effect of isoscalar pairing and tensor interaction is found; namely, the tensor force reduces the spin-orbit splittings and enhances the effect of the isoscalar pairing.