Hi, 
You can pursue diploma in computer engineering only if you meet their eligibility requirements.  Since you haven't mentioned any college, I can suggest you some colleges.
1. Lenora college of engineering 
2. Aligarh Muslim university
3. Maharajah Sayajirao university of Baroda
4. Thermostat college of engineering
5. Oriental university in Bangalore
The course is of 3 years and the fees can range between 1-3 lakhs.
Coming to your next question, domicile certificate is required so that you can get opportunities regarding job placements,  admissions etc. as it certifies your residence in a particular state.