We present Atacama Large Millimiter/submillimiter Array (ALMA) observations of eight highly excited CO (J) lines and continuum emission in two $z\sim 6$ quasars: SDSS J231038.88+185519.7 (hereafter J2310), for which CO(8-7), CO(9-8), and CO(17-16) lines have been observed, and ULAS J131911.29+095951.4 (J1319), observed in the CO(14-13), CO(17-16) and CO(19-18) lines. The continuum emission of both quasars arises from a compact region ( kpc). By assuming a modified black-body law, we estimate dust masses of Log$(Mdust/M\odot )=8.75\pm 0.07$ and Log$(Mdust/M\odot )=8.8\pm 0.2$ and dust temperatures of $Tdust=76\pm 3 K$ and $Tdust=66-10+15 K$, respectively for J2310 and J1319. Only CO(8-7) and CO(9-8) in J2310 are detected, while $3\sigma$ upper limits on luminosities are reported for the other lines of both quasars. The CO line luminosities and upper limits measured in J2310 and J1319 are consistent with those observed in local AGN and starburst galaxies, and other $z\sim 6$ quasars, except for SDSS J1148+5251 (J1148), the only quasar at $z=6.4$ with a previous CO(17-16) line detection. By computing the CO SLEDs normalised to the CO(6-5) line and FIR luminosities for J2310, J1319, and J1149, we conclude that different gas heating mechanisms (X-ray radiation and/or shocks) may explain the different CO luminosities observed in these $z\sim 6$ quasar. Future J CO observations will be crucial to understand the processes responsible for molecular gas excitation in luminous high-$z$ quasars.