You should not use car subwoofers for home designs. The requirements of a car subwoofer are different from a home subwoofer because of the cabin gain inside a car, which boosts the bass frequencies. In the home, there is no cabin gain, so you hear the driver for what it is: a flashy, expensive piece of plastic. A subwoofer for home use must have fairly SUBstantial bass response. *Subwoofers such as the Audiomobile MASS subwoofer are fine for this, but they are out of your range.
If you use this woofer, or just about any other car woofer you might think to try, you will be very disappointed. Rather, you can get woofers that will be so much better for subwoofing from Parts Express. Don't try anything smaller than 10".
AUDAX HT240G0 10" treated paper cone woofer
This one has a cool double-stack magnet structure and a treated paper cone. It also has response down to 49 Hz. This is far better than you will get with your Pioneer. It has 160-watt RMS power handling. This is about half that of the Pioneer, but car subwoofers use stiff suspensions to require more power to drive them. This also adds up to poor bass performance. The right amp to drive these is the Parts Express 120-watt sub amplifier. It can be found at:
This amplifier has a bit of boost right around 35 Hz and while is is stated 120 watts, Parts Express has measured it at 156 watts into 4 ohms. This means that you will be able to power the driver with plenty of power (many other 10" commercial subwoofers have only 100 watts) without ever blowing it out.
Use WinISD ( http://www.linearteam.org ) to design the box for a system that will serve you well. Visit http://www.diysubwoofers.org for information about loudspeaker design theory, namely ported boxes. This is what you want. Look around at some woofers that aren't just pretty pieces of plastic for a change, and you will find a whole new world of sound. But you cannot go into it thinking you are still designing a car subwoofer box, or else you will be disappointed. But if you recognize that car audio and home audio are very different universes (yet still related in some ways), then you will wind up with a very high-quality subwoofer. Designing your own speakers is fun, challenging, and easy to do.
If you don't mind spending a bit of money, move up to the Dayton Titanic 10" and a 250-watt subwoofer amplifier for uber-low bass.
BAM is correct about "cabin gain" being included in the specs of enclosed car speakers. Also, they do that a lot when listing "frequency range", which is often a useless statistic as well.
However, a speaker made for cars will have T/S, (Thiele-Small) parameters just like any other speaker. If these parameters are stated accurately, they will determine what the speaker will sound like in what size box. In this case, if this speaker is put into a 2 cu ft box, it will be 3 dB down at 34 Hz. If the efficiency is stated accurately, (89 dB @ 1W/1M), that is not too bad. And it has an excursion of almost .5 inch, which is good.
In other words, I would not rule this speaker out, especially if you can pick it up discount off it's list price of $135.
Follow BAM's advice and check out alternatives and Parts Express. If you really think this is the subwoofer for you, let me know and I will check to see the sensitivity rating checks with the Thiele-Small parameters-some companies exaggerate and that is one way to catch them.
I think this speaker is a possibility.
Here are the Thiele-Small parameters if you or anyone wants to run them through a program:
As a matter of fact I have two TS-W304c subs in an enclosure of volume 4.0cuft tunes to 35Hz. I also use Linear Team but the larger enclosure and higher Fb gives me an awesome boost that can be felt....