Calculating & Listing Permutations

This problem is doing my head in! tried doing it longhand as inexperienced with spreadsheets but is too big (for me, anyway) to work out. Can anyone help or point me in right direction.
I play badminton with 7 friends & we play as 4 sets of pairs. We play with same partner for 3 weeks playing each other pair over that time. We then change partners & repeat as above. This goes on over a 21 week period, then we start again.
I noticed that certain pairs never played other particular pairs & thought i would try to solve this problem by creating list of all possible permutations of pairs playing each other.
It was easy enough to find there were 28 possible pairings but the problem is creating a list of the groups of 4 pairings to play each other over the 7 x 3 week periods we currently play. Maybe it's not possible & we have to change our playing system? Below is current groupings.
Any help would be greatly appreciated,
PJ

1) BH & BP, Br & Ch, Da & Pa, Ge & Ja
2) BH & Br, Da & Ja, BP & Ch, Ge & Pa
3) BH & Ch, Da & Ge, BP & Br, Ja & Pa
4) BH & Pa, Ch & Ge, Ja & Br, BP & Da
5) Da & BH, Ch & Ja, BP & Pa, Br & Ge
6) Ge & BH, Br & Da, Ch & Pa, Ja & BP
7) Ja & BH, Br & Pa, Ch & Da, Ge & BP