The original sentence for the question “Which canvas appears to have been painted with a red paint?” is “This/That canvas appears to have been painted with a red paint”, and the answer would be “This one/canvas” or “that one/canvas”.
The reason why that sentence has no does is that it is the subject noun phrase (NP) that is being questioned. When, say, an object is substituted by a wh-NP, then that does (or anything like do/did/is/must, etc.) stands between the wh-NP and the subject NP, e.g.:
“He reads The New York Times every morning.” – “The New York Times” is the object, if we put a question to it, we get:
“What does he read every morning?” – does stands between the object “what” and the subject “he”.
But in the case of your canvas sentence when the wh-NP and the subject NP are the same, no do/does/did is “extracted”1 from the predicate verb, and the verb remains as it is in the original declarative sentence. One more example:
“My father likes coffee.” – “My father” is the subject NP. By asking “whose?” we put a question to the subject NP, so no does is extracted, “likes” remains as it is:
“Whose father likes coffee?” – direct word order.
In short, when the question is put to the subject noun phrase, the word order remains direct, like in the original declarative sentence, no do/does/did is added to the sentence, and only what's questioned is substituted for a wh-whord.
1 by do/does/did “extraction” I mean the transformation of the synthetic verb forms into analytic ones, e.g.: come → do come, comes → does come, came → did come.
