Solutions for the future
Because Sweden essentially has too few children, and too many old people, it has what could be called an aging population crisis. There are 2 obvious solutions for the future: encourage immigration of working age people, and encourage larger families.
A few ways to encourage larger families is to offer a cash bonus to the families with 2, 3 or 4 kids. There could also be a federally sponsored program for aspiring parents to adopt young AIDS orphans from Africa or children without parents in developing countries. These two tactics could increase the number of children, and so there would soon be more working age people. This would help reduce the aged dependency load (this paragraph human geography index).
Another potential solution is an open doors immigration policy. There are many men and women in the world who are working age but unemployed. If they were encouraged to come to Sweden, there would be more people of working age in Sweden, making a larger tax base. This would mean that there will be more money to fund healthcare and old age pensions. This could help deal with an imminent funding crisis for services for old people, and boost the economy (this paragraph from Human Geography index).
A final potential solution would be to encourage late retirement to keep a large working community (wikipedia).
Therefore the two best ways of solving Sweden's aging population crisis are encouraging large families and immigration.