"Object complement" is right (or "secondary predicate") - but there are different kinds of these beasts. And the "coffee" and "wall" examples are different kinds of object complement.

"The barista served the coffee black" is a depictive construction, expressing a property of the object at the time of the main event (verb). Other examples: "I ate the meat raw", "I left Chris angry".

"I painted the wall blue" is a resultative construction - same syntactic structure, but the adjective phrase expresses a property that the object ACQUIRES AS A RESULT of the main event. Another example: "I beat the metal flat." (Resultatives are much less common.)

Another difference between them is that a resultative can only use an Adjective Phrase, but a depictive can use other things (NPs, participial phrases). So maybe "He served the coffee in a glass" works the same way.

There are other differences between depictive and resultative secondary predicates - but rather than list them, I'll point to the book I pinched most of this from! "Lexical Categories: Verbs, Nouns and Adjectives" by Mark C. Baker - and you can see the relevant pages on books.google.com (search for "resultative", and you should find it - pages 219-221).

Oh, and his definition of a depictive secondary predicate makes me think that "cold" might be BOTH adjectival and adverbial: it is "an AP attached to the clause to supplement the meaning of the verbal main predicate, the ‎AP expressing a property of the underlying object of the clause". So it both supplements the verbal predicate and modifies the object noun.

Looks like you can have your coffee and drink it too ... :)