There isn't a trends API endpoint. One could be added, but it's not
something that is requested very often, so it's not a high priority.
Note that the kinds of stats that Trends computes can be done using
the lower-level API. All it does is things like:
http://www.google.com/reader/api/0/stream/items/ids?n=10000&s=user/-/state/com.google/read&ot=OLDEST_TIMESTAMP
(to get the IDs of all the items that were read). OLDEST_TIMESTAMP is
now - 30 days (you can go further back, but things will get slower)
http://www.google.com/reader/api/0/stream/items/ids?n=10000&s=feed/http://subscription1&s=feed/http://subscription2/...&ot=OLDEST_TIMESTAMP
(to get the IDs of the items in subscribed feeds)
By interesting the two lists you can compute the percent read for each
feed. You can also do the same with the starred, broadcast, liked,
etc. streams.
The /api/0/stream/items/ids endpoint should be quite fast, since it
doesn't need to look up and return item bodies.
Mihai