The content of a cartography table that was opened with code can't be changed. For instance, the following code is not working:

 
Inventory inv = Bukkit.createInventory(player, InventoryType.CARTOGRAPHY); // Setting the owner as null doesn't have any effect.
inv.setItem(0, new ItemStack(Material.STONE)); // This is the line that is not working
player.openInventory(inv);
However, it does work with other types of inventories such as BREWING and it also works when the player opens the cartography menu manually (right clicking a cartography table block). 

Also, if you drag and drop an item into one of the slots of the cartography table it will sometimes disappear.