There is geo-coding by zip-code centroid, but is there a zip+4 centroid which would be more granular yet not quite street-address granularity?
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Yes, there is. I work at SmartyStreets, where we validate and geocode street addresses. ZIP+4 is approximately block-level, which sounds like what you're looking for. There are some services that offer this type of geocoding, including ours, LiveAddress.
If you don't need super-precise geocoding (like you would if you were, say, going to skydive onto your buddy's rooftop), then ZIP+4 is most likely going to be the most affordable option, as well. Rooftop-level precision data has to be gathered manually (by companies like Google, etc.) and so it is very expensive.
So yes, it is possible to geocode by ZIP+4 centroid, and it would usually get you within about a street block of your target.

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