You can make estimated tax payments for anything, and you won't designate their purpose when you make them. That's because your 1040 just totals up all the taxes you have to pay, then subtracts out payments you've already made, whether through estimated taxes, withholding, or credits.
If you sell a property in another state, you will actually end up paying taxes to both states. Specifically, you'll file a non-resident return in the state whether the property was sold, and a resident return in the state where you live. Your resident state will give you a credit for the taxes paid to the other state, so you won't be double taxed.
some states do not have an income tax. those that do have various rules for when estimated tax payments are required. so if the state where the property is located has an income tax, you may need to make estimated tax payments. if you tell us the state we can tell you the rules or you can do it yourself by going to the department of revenue website for where the property is located and then read up on its estimated tax requirements.
if the state has an income tax, have you been filing annual income tax returns to report the rental activity?