I have this problem too. Did you try suggested by f54da? If you have a premium account, you can attempt to login via clementine player. May be mopidy or something else. There are many spotify-related project on github. Suddenly there is something interesting for snow leopard.
Another way is virtual machine with windows or linux. On my macbook 2010 with 10.6.8 spotify works on windows 7 via parallels desktop
My Mac currently is running Snow Leopard (10.6.8), and I would like to develop with Java 7. I downloaded the Java 7 OS X installer from Oracle's website, started to run it. Unfortunately, I was
stackoverflow.com
His compiled binaries saved my day on several occasions and I've been running that Java 7 alongside Apple's Java 6 on all of my SL machines ever since.
At the time of posting, he put his binary on bintray.com, but that repo is long gone.
The repo was called j2sdk-bundle-x86_64-u60-b19-20140622.tar.bz2
If someone needs it, you should probably try to find a way to contact him. I've tried to find his email, but I couldn't.
I also don't feel I should upload his work anywhere without his permission.
CS grad student at Purdue Fort Wayne; Interests include security, embedded systems, web dev, & vintage electronics restoration. More on my site! - wyatt8740
Since using any browser's built in password management on Snow Leopard would probably be a terrible idea, I looked for functional password managers in the Snow Leopard compatibility table. It looks like KeePassX 0.4.1 and Password Gorilla 1.4.4b (which I've never heard of and cannot find) are the only known options as far as I can tell. If someone has permissions it might be worth adding that KeePassX link to the list. It was not super easy to find, they've removed everything that old from their site. Works perfectly fine!