Nothing that involves saving the actual username/password on the user's computer is "safe"; if you seriously care about safety you just won't do it.
Then again, if you're making a sports score site or something else where security isn't paramount, cookies might just be "secure enough". It just comes down to (as you noted): "what happens if a malicious user gets access to your user's cookies?" Since that's going to be pretty rare (it requires the attacker to have physical access) if the "what happens" isn't too bad, then I'd argue cookies are "safe enough".
Ultimately though, the more popular approach for this sort of thing is just set a fairly long session timeout. The session ID will be stored in the cookies, but not sensitive password info.