Do what I did! It worked!
I know it doesn't sound appealing, but it will work. Especially if you are getting bad grades at school, or anything like that. Trust me.
Write an essay of why you deserve/need a new phone.
1st Paragraph: Introduction: Use a REALLY good grabber. Thesis: Ex. I need a new phone because it's hard to reach you when..., I think i'm responsible and my communication skills will improve with you... etc. Maybe even include a couple phones you might want, and say you'll pay half-way or something. Odds are, they'll be impressed and maybe just go buy you a phone that day.
2nd Paragraph-4th Paragraph: LOTS of details!!!
5th Paragraph: Conclusion: Leave it off with something that makes them want them to buy you a new one sooo bad. Like maybe: If you get me this phone, I PROMISE to you that I will... or our communication problems will be solved because.... etc. you get the point.
I'm sure you're parents will be impressed and they will talk to you about it.
Another idea: Make a list of phones that you might want for Christmas. Research them, and tell them how you will use it wisely and not break it, yada yada yada. Talking always works too :)
If you want to look at some of the available Verizon phones, go here. I recommend the Alias 2. It's cheap and incredibly awesome :D
http://www.verizonwireless.com/b2c/store/controller?item=phoneFirst&action=viewPhoneOverviewByDevice&deviceType=Phones&sortOption=priceSort&lid=//global//phones+and+accessories//cell+phones
By the way, if your parents are worried about the price, talk to them and see if they personally now somebody that owns a Verizon store. Seriously! Because my mom's brother owns an AT&T store, and he got me an $100 phone for $30! Consider it :)
---EDIT 9:17PM--
You should tell them to check out that website. Maybe they'll order one, saving them a trip and making them happy, because you can get a huge discount online. Put it in your essay?