Some airpots have testing stations on-premise (with results printed out in English), which I found very convenient two weeks ago in Venice,
but if you want something in Ljubljana, there is e.g.:
- UKC Ljubljana (largest hospital in Slovenia) offers testing (unspecified, but looks like PCR) for 68€ - https://www.kclj.si/index.php?dir=/pacienti_in_obiskovalci/klinike_in_oddelki/klinika_za_infekcijske_bolezni_in_vrocinska_stanja/samoplacnisko_testiranje_covid19
- ZD Ljubljana offers PCR for 100€ - https://www.zd-lj.si/zdlj/index.php?option=com_content&view=article&id=624&Itemid=2651&lang=sl
They both give you some kind of reciept, but it could be in Slovene only.
There also seem to be some private clinics available:
- Juventina where PCR test costs 85€ https://juventina.si/covid-test/
- Hippocratis Medico with 95€ PCR test https://www.hippocratis-medico.si/samoplacnisko-testiranje-covid-19/
All of these seem to require an appointment.
If you'll try to look for yourself in September, the keywords are "samoplačniško testiranje" (self-payed testing) and you can add "ljubljana" or "pcr" or "hag" (for antigen testing)