6x9's won't give you what you are looking for with bass most likely. But they will provide some fairly low mid notes that may be adequate for this particular case.
What type of headunit do you have, is it stock? And are you looking to have an amp with these speakers?
So you have a pair of 10's and you want to remove them and upgrade the rear 6x9's from the ones you have and get more bass than those powered subs? Almost certainly not going to happen (even if the 10's were crap). That's not to say you can't find a nicer pair of 6x9's that will sound better to your ear and offer mild to decent mid's and a little bass but it's unreasonable to expect them to produce more bass than having a pair of properly powered and enclosed 10's. Especially if you aren't running an external amp for those door/deck speakers.
I've had/have systems in other cars but I kind of sense you're not liking having the sub box in the trunk sucking up room if you're taking it out or maybe you don't like the weight when going to the track. The compromise I came up with for the SRT-4 was to install a small Infinity Basslink in the corner of the trunk. It's definitely not the most powerful sub out there, but it's compact, self-contained, only weighs 15 pounds, and was pretty reasonable. I combined it with a nice set of 6x9's that are crossed over for essentially a little mid's and it works pretty nice.
Your head unit and it's equalization/output can also make a pretty big difference, but if I wanted some decent bass and was in your shoes but didn't like having the 10's I'd maybe look into a good set of speakers for the rear deck as a starting point. Then power them externally with a small amp (don't rely on the head unit for power) and look into something like the factory Kicker sub or building a small enclosure properly sized for a single great 10 or 12" sub, feed it a nice supply of power, and call it a day. Your current components may have weaknesses and room for improvement but I doubt you'll be happy even after upgrading other stuff if you completely remove the subs.
Also if you don't want to run any type of separate subs you might be better off upgrading all your interior speakers and work on small things like dampening and sealing to improve the quality of what you can get out of said speakers. Get a nice set of components for the front that can provide some decent mid range then maybe look at finding a nice set of free-air enclosure 8's and modify the rear parcel shelf/deck to accept them. The 6x9's aren't necessarily bad, but due to the design of the cone can have some odd characteristics when pushed hard. A pair of quality 8's (especially 8's backed by a decent amp) might work out better for you.
I was trying to keep the budget down for my build, got a great deal on them and decided to go with some Infinity Kappa's on my car but there are a lot better/nicer speakers out there depending on your budget. You might try starting off by looking up some specs online and then match up a few speakers to your available "true" power level that you'll have to feed them. By true power be wary of the "generous" 50x4, 60x4 watts, etc. ratings you might get from a head unit manufacturer (if that's what you plan to continue using). Also watch out for speakers rated to handle way higher power then they really can, so pay attention to the minimum suggested power ratings more than peak numbers. Then look at other things like cone and surround material, frequency response, etc., but most importantly go to a real stereo store (preferably not Best Buy, Circuit City, etc.) and take some of your CD's with you and sample a few different speakers. Everyone's ear is going to be different on what they like.
There's one other thing to note if you still remember how the stock head unit and speakers sounded and are using that as a point of reference. They can come across as very punchy and I know many people that aren't really into audio who think it's a great setup. And for a stock system it isn't too bad, but the equalization curve they apply for the speakers is mostly responsible for this and not quality of speakers and head unit power. With just the upgraded front components and rear 6x9's (i.e. no sub connected) you might have thought I'd lost bass response if you got in my car, even with the small external amp, but start cranking it up and the stock setup would have started clipping and producing some nastiness when the aftermarket setup starts to shine. Like I already mentioned the head unit output/EQ can make a big difference as well and swapping different HU's that I have can cause some noticeable changes in overall sound reproduction on my setup.
get another $35 or so and buy 2 bulk packs of dynamat xtreme, or similar items (second skin, raammat). do the trunk, rear deck and front doors. you will be amazed how much better your system sounds. it even made the factory system have enough sound to turn a few heads as i rode by (well, not factory hu, but speakers).
this is always my first step as it will not only help the audio but also the road noise. it's amazing what enters the cabin via the doors and wheel wells.
Tang Band makes two different 6x9 subs. They won't play the mids and highs (your front speakers can handle that) but they do pretty well on the lows and they fit a standard 6x9 cutout. They do need an amp, though not much of one.
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