These are difficult problems to optimise. There are some software packages out there for tennis clubs that may help (try an internet search for "tennis doubles sofware" or similar search term), I have not any experience using these so can't make any recommendations. But before I bought I would want to know how well it might handle the 10 men/11 women situation.
Alternatively, if you have 10 men and 10 women, then you will find a
list of 45 matches here. Don't be put off by the fact that it is for husbands and wives, just read instead men and women respectively. I don't know how many rounds of 4 games you want, but I think it might be possible to pick out 15 matches and arrange them as 5 rounds of 3 matches, so that nobody plays twice in a round and that everyone gets 3 games.
Hope that helps a little,
Ian.