For the actual addresses and phone numbers of car rentals in Tallinn, you can visit the website of Tallinn's airport. You'll find the details at this link. To inquire about car rentals in Tallinn without a deposit, you can call them directly.
Car rentals in Tallinn, available 24/7, are usually best arranged in advance. Renting a premium car, such as a sports coupe valued at 170-180 thousand EUR, can cost around 4000 EUR for a 2-day rental. However, with some effort, you can find budget-friendly car rentals in Tallinn for as little as 10 EUR per day.