Take a standard round-robin for 6 players (I have used the 'balanced' one you can get by following the schedules link at the top of this page) and then rearrange the order of the three columns, rotating by one place for each block of 5 rounds. A team's opponents will come around in the same order for each block of 5 so you might like to randomize the order of rounds 6 to 15 to avoid this.
S1 S2 S3
Round 1: 36 12 45
Round 2: 62 53 14
Round 3: 43 25 61
Round 4: 24 31 56
Round 5: 15 64 23
Round 6: 45 36 12
Round 7: 14 62 53
Round 8: 61 43 25
Round 9: 56 24 31
Round 10: 23 15 64
Round 11: 12 45 36
Round 12: 53 14 62
Round 13: 25 61 43
Round 14: 31 56 24
Round 15: 64 23 15