You should specify in your lease or rental agreement how rent must be paid: by cash, check, money order or electronic transfer. 

For most landlords, rental checks are routine.  If a tenant does not have a checking account or has bounced too many checks, you may want to require a certified check or money order. 

You should never accept post-dated checks.  The most obvious reason is that the check may never be good. Your have absolutely no assurance that necessary funds will ever be deposited in the account, or be available when the time comes to cash the check.  Far better to tell the tenant that rent must be paid in full on time and to give the tenant a late notice if it isn't.

If a tenant pays rent by cash, money order or any form other than a personal check, state law requires you to give the tenant a written receipt. (RPL235-e(a). The rent receipt must contain: the date rent was paid/the amount of rent paid/the address of the tenant’s rental unit/the time period for which rent is paid/the signature and title of the person who accepted the rent. 

Be sure to keep copies of rent receipts in tenant files. These may be  important evidence if you and the tenant end up in court in a rent dispute. If you have been burned by bounced checks from a particular tenant, you may want to decree that from now on, you will accept nothing less than a certified check or money order. Be careful. It may be illegal to suddenly change your terms for payment of rent without proper notice to the tenant.