I tried to configure a private network with Slackware boxes but I did get into trouble. I get the same error with a box (ricardson/slackware64-14.1-minimal) from the Atlas catalog and with a box I created from scratch. I am using Vagrant 1.7.4 and VirtualBox 4.2.24.
The error message is the following:
Configuring and enabling network interfaces... Vagrant attempted to execute the capability 'configure_networks' on the detect guest OS 'linux', but the guest doesn't support that capability. This capability is required for your configuration of Vagrant. Please either reconfigure Vagrant to avoid this capability or fix the issue by creating the capability.
This error occurs when adding a vm.network with "private_network" attribute. Port forwarding does not cause any problem.
I haven't find the reason of this problem yet but it seems clear that is it related to the box itself. Slackware seems to be missing something. I can switch to another box but I would be very interested to understand that issue. Any help would be appreciated.