You shouldn't have any problems. The first three rounds from a standard Berger pairing table from a 12 team round robin illustrate this. For each round play the first two columns, then the middle two, and then the last two. There will be a minimum of one game out for each team although the average will be two.
1: 1-12 7-6 11-2 8-5 10-3 9-4
2: 12-7 2-1 6-8 3-11 5-9 4-10
3: 2-12 8-7 1-3 9-6 11-4 10-5
If you have 14 or 18 teams you can play the last game of one round at the same you have the first game of the next round and there will be even more time between each team plays.
HTH