2 quick questions

Sorry about the repost. The first thread got mixed up... First, I'm in a tight space, and was wondering if I should go with an Alpine Type-E SWE-1041 (10") and put it in a 1 cu.ft. ported box or a Alpine Type-E SWE-1241 (12") and put it in a 0.85 cu.ft. sealed box. I'm looking for some nice, deep boom. Also, is it possible to use a 2 channel amp on a svc sub?

Listen to both subs at your local dealer and pick the one you like best....if it is spec'd to go into a sealed enclosure of that size.  Yes, you can use a two-channel amp to power any speaker or combination of speakers as long as the impedance load is comfortable for the amp to handle.  Your SVC sub should be 4 ohms or 8 ohms to be bridged across the two channels.

The sub is 4ohms. So with a 2 channel amp, would I just run to positive wires and 2 negative wires to it? or what?

Look at the diagram in your amp manual for 'bridged' configuration.  It is one pos and one neg from the speaker terminals to the bridged terminals of the amp.