Is someone with a masters in CS eligible to apply to a CS masters program in another country? I've completed my Masters in Computer Science in India. Here we've had no specialization as such and the subjects assigned have been as per University rules. Now I feel the need to specialize in my area of interest and have found Universities in the US that will allow me to choose subjects that align with my interests. Am I eligible for applying to said universities? 

Note - These subjects are still in the Computer Science department in these Universities :( 

Will the fact that they're in a different country be the exception wherein pursuing a second Masters isn't a problem?
The issues you mentioned in your question should be covered in your Statement of Purpose. That is, you should be willing and able (as you did), to explain why you want to "repeat" the degree (you're not really repeating the courses).

Hopefully, your schools of choice would consider you "superprepared," having completed many courses, but not the ones you plan to take. The danger is if there are weaknesses in your test scores or your grades, it could work the other way by showing that you are a "less good" student who needs to repeat courses.