Trade rights are influenced mainly by your Diplomatic Skill. Expanding your SoI, and they will come fast and easy. Other factors are essentially the same as with acquiring Trade Leagues. Good relations are also important, especially if you want to keep the rights for a long time. Religion and Proximity to your CoT is also considered, and nations with CoTs will never give you Trade Rights, though countries with whom you've acquired trade rights before they acquired a CoT (ex: whoever forms Russia) will usually keep giving you Trade Rights for some time after acquiring a CoT. However it should be noted that Trade Rights are bugged so shouldn't be relied upon.