try the intertubes! in particular, visit the googles!
enter something crazy, like "sweden cycling maps"
or maybe "swedish cycling federation."

you find stuff like: The Best European Bicycle Maps

SWEDEN

Lantmäteriet, scale 1:100.000 (blue series)
113 sheets cover Sweden
Estimated price 6-9,- Euro (50-70,- Dkr)

Lantmäteriet, scale 1:200.000 (red series)
23 sheets cover Sweden
Estimated price 9-11 ECU (67-86,- Dkr)

The maps are the official Ordnance Survey maps of Sweden. The 1:100.000 maps have excellent detail. They show contour lines, youth hostels, camping sites. My suggestion is to buy these maps for southern Sweden.

If you are going long distances, or if you are travelling north of Gothenborg you may not need all the detail in the blue maps as there simply are fewer roads to the north. you may settle for the red, scale 1:250.000 series, which has an amazing amount of information in relation to the scale. However, they do lack camping sites and youth hostels. (But remember the "allemansret" whereby you may camp anywhere as long as you do not disturbe anyone).

Sweden not only has a national bicycle route from north to south, but also several regional bike routes - for example along both the eastern and western coastline. (Ystad-Stockholm-Örnsköldsvik) and (Helsingborg-Norwegian border). Contact the local tourist office. Ask for the 24 page brochure "Cykelleder i Sverige" (3,- ECU). It gives a brief discription of the many bicycle routes in Sweden.

Here's a pick of some of the local bike-route brochures:
The West Coast Route (Helsinborg - Norwegian border)
- Cykelleder i Nordvestra Skåne, 1:250.000
- Hallands Cykelleder, 1:250.000
- Cykelsporet Bohuslän, 1:250.000

The East Coast Route (Ystad-Stockholm-Örnsköldsvik)
- Cykelspåret langs Ostkusten (Ystad-Stockholm) 1:300.000
- Cykelspåret langs Ostkysten (Stockholm-Örnsköldsvik) 1:500.000

Göta-Kanal: The Swedish Waterways
- Västgötaleden, 1:250.000
- Eastgötaleden: Motala-Söderköbing