Partition magic should have a tool for resizing your windows partition (either fat32 or ntfs)
All you really have to do is open up space for a partition, and during the slackware installation you can use fdisk to create and ext3 partition, and Linux swap partition. If you aren't comfortable with the fdisk command, then partition magic should have sufficient tools also.
After you have made your partitions, you can just boot up to the install cd, and it will guide you through the installation process. When it asks you wehere you want to install Slack, just pick the one that is labeled ext3 or Linux. it will also about your swap partition, and you can give it the right name there also.
Exactly what error did you get when you tried to make the swap partition? if partition magic isn't working, then you can download a trial version of bootitng from
www.terabyteunlimited.com/bootitng.html .
boot it ng is shareware, so you'll have to ditch it after 30 days, but it has powerful resizing and booting tools.
good luck,
~Andrew
ps make sure you toggle the bootable option for the linux partition, otherwise it will boot to windows without giving you a choice after you install.