I can't buy the property in Falkreath

You don't buy the house from the jarl, you buy it from his steward. Additionally, when Siddgeir is jarl, you have to have complete the quest Kill the Bandit Leader from him.

Once you have done so, his steward will let you purchase the land.

You have to talk to the steward if you want this house. If it still doesn't have the option, you might have:

this will make Siddgeir's disposition low and you won't be able to buy it since he hates you. The only way to fix this is side with the Stormcloaks in the Civil War and complete the questline so the Jarl and Steward will be replaced and you can assist the people and then talk to them about the house.