You'll probably want to know more about the cabinet as it is now to get noticably better results than you're getting now.
You'll want to know what frequency the drivers are crossed over at, or at least have a rough idea. If possible, you want a tweeter with a Resonant Frequency(fs) such that the crossover frequency occurs 2-4 times above it, in terms of Hz. With a driver that has an fs of 1000hz, a crossover point from 2000-4000hz would be ideal. There's a lot of info about this sort of thing online, even on this forum; hopefully that'll get you on track.
Also, you'll want to match the relative SPLs of your 1 tweeter to that of your 6 10" speakers. Basically, is it going to be loud enough? You feel like you're driving your current one too hard, so do your homework on this. Tweeters generally have high output though, and many will do the job.
Check the impedance! Make sure you're not changing the impedance of the speaker(tweeter) load -at least, not making it lower-
Sites like Partsexpress.com have a variety of speakers available that will do the job, and the prices aren't bad. What size is the hole you'll be filling? Are you able/willing to change the hole to accomodate a certain driver? There are many questions to answer.