Hola,
There is a nice store called Säkerhetsbutiken,
http://www.sakerhetsbutiken.se , which specializes in child safety of all kinds. It's located about 1 mile form center of the city. The site is all in Swedish but they do have a page where you can book a seat via email. You didn't mention how old your son was but they do have infant seats, regular rf chair up to 55 lbs. and booster seats. I would just send them an email in English and explain what you need. Everyone here speaks English so it's no problem.
Normally, I advice people not to rent seats. But the seats you will find here are usually of very high quality and not some worn out crap. But, I would definitely write an email to the store way ahead of time and ask them specifically what kid of chair you will be getting. Don't confuse this rental with the normal Avis, Dollar etc. rental where poor seats can be found.
Infants seats are about $15/weekwith deposit of $100-ish, regular rf seat $25/week with $250 deposit. In case you prefer rental from another store, I'm sure we can find other sources.
Please let me know if you need any assistance. And thanks very much for thinking about using a car seat for you son!:thumbsup: