Your CIBIL is already good. What CC issuers notice while issuing:
1) Payments on time (updated every quarter). So do the payment before time only.
2) Credit utilisation. You should show it like you are using maximum 10% (5% if you can) of your credit limit. All other payment should be done before bill generation.
3) Your credit history. You have to use your OneCard 3-6 months (atleast) to get a new unsecured card while keeping above 2 points in mind.
And after 6 months, if you're above 21, give a try to ICICI Apay Card. They're very lenient while providing cards if your credit score is good.
Till then, don't do so many enquiries as it affects your credit score/profile.