I think you can use the standard round robin twice and just swap around the games associated with each column. For example:
Rounds 1-5
Fifa Darts
(1 4) (2 3)
(3 5) (1 2)
(2 4) (1 5)
(1 3) (4 5)
(2 5) (3 4)
Rounds 6-10
Darts Fifa
(1 4) (2 3)
(3 5) (1 2)
(2 4) (1 5)
(1 3) (4 5)
(2 5) (3 4)