I am not eligible for engineering... are there any private colleges in which i can get into engineering through management quota?

NO.... and a BIG fat NO Aiming for some thing which you are not rightfully entitled is not a correct decision and the degree earned that way might not be of any use in future. So plz, leave that and think of something which motivates you and inspires you. Mark my words, one day you'll be successful

you didnt made it clear how you are not eligible for engg... but still, for your ans, there are a lot of private univ... u might get admission.