I guess that you also want to balance the opponents in some way, so the problem is a hard one. I can offer the schedule below which comes close, but the number of games each week varies.
[(A03 A09):(B05 B07)] [(A04 A10):(B06 B08)] [(A05 A07):(B04 B10)] [(A06 A08):(B03 B09)] [(A01 A02):(B01 B02)]
[(A03 A10):(B08 B05)] [(A04 A09):(B07 B06)] [(A05 A08):(B09 B04)] [(A06 A07):(B10 B03)]
[(A01 A05):(B09 B07)] [(A02 A06):(B10 B08)] [(A07 A09):(B06 B02)] [(A08 A10):(B05 B01)] [(A03 A04):(B03 B04)]
[(A01 A06):(B08 B09)] [(A02 A05):(B07 B10)] [(A07 A10):(B01 B06)] [(A08 A09):(B02 B05)]
[(A01 A09):(B04 B08)] [(A02 A10):(B03 B07)] [(A03 A07):(B01 B09)] [(A04 A08):(B02 B10)] [(A05 A06):(B05 B06)]
[(A01 A10):(B07 B04)] [(A02 A09):(B08 B03)] [(A03 A08):(B10 B01)] [(A04 A07):(B09 B02)]
[(A01 A03):(B10 B06)] [(A02 A04):(B09 B05)] [(A05 A09):(B03 B01)] [(A06 A10):(B04 B02)] [(A07 A08):(B07 B08)]
[(A01 A04):(B05 B10)] [(A02 A03):(B06 B09)] [(A05 A10):(B02 B03)] [(A06 A09):(B01 B04)]
[(A01 A07):(B03 B05)] [(A02 A08):(B04 B06)] [(A03 A05):(B02 B08)] [(A04 A06):(B01 B07)] [(A09 A10):(B09 B10)]
[(A01 A08):(B06 B03)] [(A02 A07):(B05 B04)] [(A03 A06):(B07 B02)] [(A04 A05):(B08 B01)]
above there are 10 weeks of play, alternating between 5 and 4 games per week. Each player receives one bye round, so they only play for 9 out of the 10 weeks. All 45 possible within team partnerships should occur exactly once. Each player has 18 opposition pairings, and plays against all opposition players at least once and at most twice. The schedule can also be played in 11 weeks, by moving the 5 games in the last column to an 11th week, giving 10 weeks of 4 games per week, and 1 week with 5 games.
Hope that helps.
