Is this a place you have owned for awhile and not raised rents or a property that you just bought? I think raising rent is not a difficult thing to do if you do it regularly. I raise rents about 3% per year or what ever the CPI is if that is higher. Just write a letter to existing tenants in a property you have owned offering a new lease with the new rent amount.
For tenanted properties that you are buying, the matter of existing leases should be dealt with before closing. The tenant should be notified by the seller that they intend to sell the property. When they accept your offer, you can send the existing tenant a letter and offer to issue a new lease at the new rent amount. The tenant will have the option to stay and pay the new rent or to move out. You are not the leaseholder on the old lease and should execute a new lease with the tenant so that is only fair and the best way to get a cooperative tenant. If you have already signed and taken over the property, you should follow the same process but given them a month notice if they decide to move.