Motivated by the recent discovery of superconductivity at 16.3 K in layered oxychalcogenide Na₂₋ₓV₂Se₂O we investigate pairing instabilities in the broader family of layered materials composed of V₂O planes, believed to exhibit altermagnetic order in their monolayer form. Even though the bulk family members KV₂Se₂O and Rb_(1-δ)V₂Te₂O are likely conventional antiferromagnets that show only surface altermagnetism, our analysis predicts exotic equal-spin triplet superconductivity as the dominant pairing instability in these materials. This is a consequence of their unique magnetic and sublattice structure that renders electron bands incompatible with conventional spin-singlet pairing. The predicted triplet superconducting phases are topologically non-trivial and capable of supporting spin-polarized persistent currents, properties potentially useful in technological applications.