I’m not really sure what your trying to do, but for your example I would argue that writing 10+ crawlers/scrapers is a perfectly good solutions.
Training deep networks such as CNNs require large amount of data to get good results. Where do you get that training data from? In principle what you’re do is sequence labeling, with each token/word/tag/etc. in your HTML string is associated with a label (similar to named entity recognition). But again, this is arguably not an easy task to learn.