The property is held by your wife. It is registered in her name and she has the right to do anything with it. Now as she is an physical indisposition and she cant move much, you can take the responsibility on her behalf and can the agreement done. You can ask your wife to give you the power of attorney specially regarding this agreement and you can then proceed on with the agreement.
You can request your wife, to give you the power of attorney and then on her behalf, you can make the agreement. Or else, you can make the agreement from a reputed lawyer or a real estate agent and then you can get the signatures of both your wife and the tenant. In this way, you can make your wife sign the agreement. To authenticate the agreement, both the landlord and the tenant ought to sign the agreement in the presence of two people who are non-beneficiaries of the property and will sign on the agreement as witnesses.
You can make the rent agreement and receive the rent only if your wife authorises you to do so. Otherwise, you cannot do it. In your case, if you have a good understanding with your wife and you both agree on things, the best possible situartion will be to execute the Power of attorney in your favour by the wife.
Reference: Rent Control Act, 1948