I had little trouble in buying the Turks friendship at the begining of the campaign. They were desperate for a safe border, which suited me fine. Both annoying southerly neighbours declared war on me but to little effect. A few extra units in the nearby town were enough to stop them even approaching.
When Sweeden decalred war, I was able to take St. Petersburg and that was pretty much the end of any credible threat from them....
Maybe I was just extra lucky in my campaign?