In a way, everything which is possible in GAP is also possible in Sage, as Sage starts up a GAP subprocess and communicates with it. So you need not have Sage bindings for every GAP function. E.g. you can do
sage: g=SymmetricGroup(7)
sage: gap("Orbits("+str(g._gap_())+","+str(tuples([1..7],2))+",OnTuples)")
[ [ [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 4, 4 ], [ 5, 5 ], [ 6, 6 ], [ 7, 7 ] ],
[ [ 1, 2 ], [ 2, 3 ], [ 2, 1 ], [ 3, 4 ], [ 1, 3 ], [ 3, 2 ], [ 4, 5 ],
[ 2, 4 ], [ 4, 3 ], [ 3, 1 ], [ 5, 6 ], [ 3, 5 ], [ 1, 4 ], [ 5, 4 ],
[ 4, 2 ], [ 6, 7 ], [ 4, 6 ], [ 2, 5 ], [ 6, 5 ], [ 5, 3 ], [ 4, 1 ],
[ 7, 1 ], [ 5, 7 ], [ 3, 6 ], [ 1, 5 ], [ 7, 6 ], [ 6, 4 ], [ 5, 2 ],
[ 7, 2 ], [ 6, 1 ], [ 4, 7 ], [ 2, 6 ], [ 1, 7 ], [ 7, 5 ], [ 6, 3 ],
[ 5, 1 ], [ 6, 2 ], [ 3, 7 ], [ 1, 6 ], [ 2, 7 ], [ 7, 4 ], [ 7, 3 ] ] ]
Nowadays (Sage version 8.6 or newer) one can do
sage: g=libgap.SymmetricGroup(7)
sage: g.Orbits(tuples([1..7],2),libgap.OnTuples)
[ [ [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 4, 4 ], [ 5, 5 ], [ 6, 6 ], [ 7, 7 ] ], [ [ 1, 2 ], [ 2, 3 ], [ 2, 1 ], [ 3, 4 ], [ 1, 3 ], [ 3, 2 ], [ 4, 5 ], [ 2, 4 ], [ 4, 3 ], [ 3, 1 ], [ 5, 6 ], [ 3, 5 ], [ 1, 4 ], [ 5, 4 ], [ 4, 2 ], [ 6, 7 ], [ 4, 6 ], [ 2, 5 ], [ 6, 5 ], [ 5, 3 ], [ 4, 1 ], [ 7, 1 ], [ 5, 7 ], [ 3, 6 ], [ 1, 5 ], [ 7, 6 ], [ 6, 4 ], [ 5, 2 ], [ 7, 2 ], [ 6, 1 ], [ 4, 7 ], [ 2, 6 ], [ 1, 7 ], [ 7, 5 ], [ 6, 3 ], [ 5, 1 ], [ 6, 2 ], [ 3, 7 ], [ 1, 6 ], [ 2, 7 ], [ 7, 4 ], [ 7, 3 ] ] ]
Are you saying that you want the orbits of $G$ on $A\times A$ ? Such orbits are usually called orbitals. GAP can do this for you, e.g. using its package called GRAPE.
But can it be directly done in sage?
I've written the answer below :)