I would work with copies of the 7 round schedule for 8 players (follow the schedules button near the top of this page). Let's say players 5 and 6 are the two that do not play each other and the last round is removed. So there are 6 good rounds of play. Any permutation of the player numbers in the 7 round schedule will also be another valid schedule, but if you can permute the player numbers in such a way, that the game (5 6) is in a different round from the three games (1 2) (3 8) & (4 7), then it should now be easy to find your 10 rounds of play, simply take the 6 good rounds from the first schedule and add any 4 rounds from the second that cover the three games described above and exclude the round with the game (5 6).
