There is a good set of examples of binomials or word pairs in this OM page
I hope you don´t get sick and tired of the ups and downs of English vocabulary. They are just part and parcel of the rich English vocabulary and although they create doubts that the BBC tries to answer they will show off your advanced level nicely if you can include them in your writing and conversations. Here is by and large a good list of English word pairs. Click here for another comprehensive list that includes some trinomials
Practice some exercises little by little and you will progress in leaps and bounds.