hsr////////////////////////////////////////////////////////////
중간에 추가하세요.
canvas.TextRect(Rect, Rect.Left, Rect.Top, cells[m, 2]);

procedure TForm1.StringGrid1DrawCell(Sender: TObject; ACol, ARow: Integer;
  Rect: TRect; State: TGridDrawState);
  var
  m:integer;
begin
    with StringGrid1 do
    begin
             for m:=1 to StringGrid1.ColCount do begin
               Rect :=StringGrid1.CellRect(m,2);
               Canvas.Brush.Color := clYellow;   // 배경색을 바꿀때 사용
               Canvas.FillRect(Rect);
               canvas.TextRect(Rect, Rect.Left, Rect.Top, cells[m, 2]);
             end;
    end;
end;

---------------------------------------------------
그런데 Rect :=StringGrid1.CellRect(m,2); 는 2번째 줄에만 색칠하실건지요
그럼 간단히 for문 돌릴 필요없이 하세요

   with StringGrid1 do begin
       if (ARow = 2)and(ACol<>0) then begin
          Canvas.Brush.Color := clYellow;   // 배경색을 바꿀때 사용
          canvas.TextRect(Rect, Rect.Left, Rect.Top, cells[ACol, ARow]);
       end;
    end;

팁을 찾아보니까..이렇게 되어있네요.

    with (Sender as TDBGrid).Canvas do begin
       Brush.Color := clRed;
       FillRect(Rect);
       TextOut(Rect.Left, Rect.Top, Field.AsString); <-- 요게 없는것 같군요.
    end;