oops, without reading the spoolers I didn't notice the first two rows were given!

Taking that into account...

:- use_module(library(clpfd)).

different_lists([A|TA], [B|TB]) :-
    ( A #\= B ; different_lists(TA, TB)).

all_different_lists([]).
all_different_lists([A|T]) :-
    all_different_lists(T, A),
    all_different_lists(T).

all_different_lists([], _).
all_different_lists([B|T], A) :-
    different_lists(A, B),
    all_different_lists(T, A).

solve([Row1, Row2, Row3, Row4, Row5, Row6, Row7]) :-
    
    Row1 = [A1, A2, A3, A4, A5, A6, A7],
    Row2 = [B1, B2, B3, B4, B5, B6, B7],
    Row3 = [C1, C2, C3, C4, C5, C6, C7],
    Row4 = [D1, D2, D3, D4, D5, D6, D7],
    Row5 = [E1, E2, E3, E4, E5, E6, E7],
    Row6 = [F1, F2, F3, F4, F5, F6, F7],
    Row7 = [G1, G2, G3, G4, G5, G6, G7],

    Col1 = [A1, B1, C1, D1, E1, F1, G1],
    Col2 = [A2, B2, C2, D2, E2, F2, G2],
    Col3 = [A3, B3, C3, D3, E3, F3, G3],
    Col4 = [A4, B4, C4, D4, E4, F4, G4],
    Col5 = [A5, B5, C5, D5, E5, F5, G5],
    Col6 = [A6, B6, C6, D6, E6, F6, G6],
    Col7 = [A7, B7, C7, D7, E7, F7, G7],

    Row1 = [2, 1, 0, 0, 2, 2, 1],
    Row2 = [0, 2, 2, 1, 1, 0, 2],
    % Col1 = [2, 0, 0, 1, 1, 2, 2],

    global_cardinality(Row1, [0-2, 1-2, 2-3]),
    global_cardinality(Row2, [0-2, 1-2, 2-3]),
    global_cardinality(Row3, [0-2, 1-2, 2-3]),
    global_cardinality(Row4, [0-2, 1-2, 2-3]),
    global_cardinality(Row5, [0-2, 1-2, 2-3]),
    global_cardinality(Row6, [0-2, 1-2, 2-3]),
    global_cardinality(Row7, [0-2, 1-2, 2-3]),

    global_cardinality(Col1, [0-2, 1-2, 2-3]),
    global_cardinality(Col2, [0-2, 1-2, 2-3]),
    global_cardinality(Col3, [0-2, 1-2, 2-3]),
    global_cardinality(Col4, [0-2, 1-2, 2-3]),
    global_cardinality(Col5, [0-2, 1-2, 2-3]),
    global_cardinality(Col6, [0-2, 1-2, 2-3]),
    global_cardinality(Col7, [0-2, 1-2, 2-3]),

    all_different_lists([Row1, Row2, Row3, Row4, Row5, Row6, Row7]),
    all_different_lists([Col1, Col2, Col3, Col4, Col5, Col6, Col7]),

    label([A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7, C1,
+ C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7, E1, E2, E3, E4, 
+E5, E6, E7, F1, F2, F3, F4, F5, F6, F7, G1, G2, G3, G4, G5, G6, G7]).
    
tryme :-
    writeln('searching...'),
    time(solve(S)),
    writeln(S).
[download]

and running it...

?- tryme.
searching...
% 281,537 inferences, 0.180 CPU in 0.183 seconds (98% CPU, 1564094 Lip
+s)
[[2, 1, 0, 0, 2, 2, 1], [0, 2, 2, 1, 1, 0, 2], [1, 0, 0, 1, 2, 2, 2], 
+[1, 2, 1, 0, 0, 2, 2], [0, 1, 2, 2, 2, 0, 1], [2, 0, 2, 2, 1, 1, 0], 
+[2, 2, 1, 2, 0, 1, 0]]
true.
[download]

So, the problem is solved in less than 200 miliseconds!

update: constraints reordered to improve performance slighly