I've been playing lead guitar in a modern country band semi-professionally for about 4 years now (It's how I put myself through college

). Country is often difficult for rock guys to figure out because the tonal aesthetics are totaly different! Its a lot more major tonality based. The most common sounds that you hear that make country sound like country are mixtures of mixolydian and ionian modes. There is a lot of emphasis on the minor 3 moving to the major 3 and the b7 moving up to the 7. Try this lick in E all straight 16th notes around 120 bpm
-7/9-7-----7---------------------------------------------
-------8-9--8-7------------------------------------------
----------------9-7^(8)-9-7----------------4\2---1------
-----------------------------9-8-7---4-5-6-----4---2---2
-----------------------------------7------------------4--
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Here's another good one in G using both the minor 3 resolve to major 3 and b7 to 7:
-10---------------------------
-11^(12)----------------------
----------12-10---10^(11)-12
----------------12------------
-------------------------------
I could go on and on They're so fun!
Pay attention to the different tonalities used and how much different they are from other styles such as rock, those differences are what give any style its uniques feel and sound.
Ok a couple more!
Here's a cool and easy way to sound like a pedal steel bend in A. Let all three notes ring together as you bend the 2 up to the 3 on the G string
-------------------------------
-------------------------------
---------------------4^^(6)---
------------------7-----------
--------------7---------------
------------------------------
This one uses some fun hybrid picking in C use the pick for the single notes on the D string and your middle and ring fingers to play the double stops on the G and B strings use a very staccato sound to all notes
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-------11----10-----8--------------------
-------12----10-----8^9-------8---9---------
--/10-----10----10-------10---7---10-----------
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Ok! I really could go on forever I need to stop!