You there are various private colleges where you can apply, but I would recommend you to reattempt next year and grab a better college if possible. Be careful while choosing your institute as it will provide you with exposure and the environment required for grooming yourself right.
Careers360 has curated a complete list of colleges where you can apply, follow the link: https://bschool.careers360.com/articles/where-can-i-apply-60-percentile-in-cat
Hope this helps,
All the best!
It's very difficult to get in with this pervpercen on CAT.
I Would suggest to focus on other entrance exam.
All the best
51 percentile on MBA is relatively low for general category