Even you would like to marry her as pr Muslim personal act, the marriage can be registered only under foreign marriage act or special marriage act since she is a foreign citizen.
For getting legal validity for the marriage the marriage has to be registered under special marriage act by following the procedures meant for it accordingly.
In India, civil weddings are governed by the provisions of The Special Marriage Act (1954). Under the Act, there’s a 30 day residency requirement, which means that either the bride or the groom has to be living in India for at least 30 days prior to applying to the local registry office to get married. For foreigners, this is evidenced by a certificate from the local police station.
You’ll need to submit your own documents to prove your identity.
In addition, evidence of eligibility to be married is usually required. Anyone who hasn’t been married should obtain a single status affidavit (in the US), a Certificate of No Impediment (in the UK), or Certificate of No Record (in Australia). If you’re divorced, you’ll need to produce the Decree Absolute, or if you’re widowed, a copy of the death certificate.
If no objections to the marriage are received within 30 days of the application, a civil ceremony at the registry office can then take place. Three witnesses are required, who have to provide passport sized photographs, as well as identification and proof of address. The marriage certificate is usually issued a couple of weeks after the wedding.
Since your wife will be here on a tourist visa, you have to convert her visa from a tourist visa to a short visit visa (valid for one year). For this you may have to visit the Foreigners Regional Registration Office (FRRO). For this one has to go to Delhi at the following address: The Director (Foreigner), Ministry of Home affairs, Visa Facilitation Centre, Jaisalmer House, 26, Mansingh Road, New Delhi - 110 011. She should carry the original marriage certificate, and both your passports. A fresh visa application form has to be submitted. As a note, to add that a tourist visa is extendable by 45 days (Max) if an Indian citizen gives an undertaking in writing. The undertaking form is available with them.