From the graviton-graviton scattering amplitudes calculated perturbatively in quantum gravity to the oneloop order, we develop further a formalism that allows one to calculate infrared-finite partial-wave amplitudes fulfilling perturbative unitarity. As a result of this process a parameter dubbed ln𝑎 emerges that separate between infrared and typical external momenta. The resulting partial-wave amplitudes are next unitarized by employing the Inverse Amplitude Method and the algebraic-𝑁∕𝐷 method. Then, the graviball resonance, with a similar pole position, is confirmed in the 𝑆-wave partial-wave amplitude for all unitarization methods, also with respect to the unitarization of only the leading-order amplitude. Although the spectrum of the theory is independent of the specific value of ln𝑎, the requirement for a well-behaved unitarized effective field theory of gravity identifies the optimal range of ln𝑎 for our next-to-leading-order calculations as 0.5 ≲ ln𝑎≲1.7. Briefly, we discuss the 𝐷-wave scattering that is weaker than the 𝑆-wave scattering, repulsive and non-resonant for ln𝑎 ≈1.