How to load and apply planet osm diff?

Applying diffs is much slower than the full planet load; if you want to apply diffs for a few months then it is almost certainly going to be faster to drop the database and load it again. (It could be that applying one day's worth of diffs takes more than a day!)

Having said that, here's how to update:

1. Find out the highest node ID you have in your database (if you have used flatnodes, then running nodecachefilereader will tell you, else do a select max(id) from planet_osm_nodes).
2. Get https://svn.openstreetmap.org/applications/utils/whichdiff/whichdiff.pl
3. Run perl whichdiff.pl [highest_node_id]
4. Install osmosis, run osmosis --rrii do initialize a status directory, and copy the state.txt file that you got in step 3 into that directory. Check the max_interval setting in configuration.txt and perhaps set it to 3600 (update only one hour) initially to see how long it takes to update one hour. You can re-run the following as often as you want until you arrive at the current end of the data:
5. run osmosis --rri --write-xml-change mydiff.osc.gz
6. load mydiff.osc.gz into your database using the same osm2pgsql and same options as you used when doing the initial load, just use --append istead of --create