Old iPod touch 2nd gen can not connect to iTunes store for some reason.

How do I download from my iTunes library onto my old iPod?

Note that even though you can no longer access the iTunes Store, both iPods can still be used with iTunes (the programme, not the store) to enable adding music from your iTunes Library to the devices.

AndyBrookes wrote:

How do I download from my iTunes library onto my old iPod?

The same way as in the past. Note that if you have synchronised this iPod with a different iTunes Library, you will see a warning that if you sync the iPod with your current Library, all the music on the iPod will be removed. It will happen (and you cannot copy music on the iPod back into an iTunes Library):

• connect the iPod to your computer and tap the iPod icon that will appear in the iTunes window:

• this will show you the Device/Settings/Summary pane. Switch to the Device/Settings/Music pane (1.) as shown in the screenshot below:

• click on the Sync Music box (2.) so that a tick (checkmark) appears in the box
• in this step (3.), if you select:
  • Entire music library - iTunes will add all the music in the library to the iPod (you will not see any of the sections number 4 in the screenshot)
  • Selected playlists, artist, albums and genres - this will open up all the sections numbered 4, where you can choose the items that you wish to add to the iPod
• tap the Sync (or Apply) button in the lower right corner of the iTunes window (not shown in the screenshot)

That's it.

For security reasons 4th generation and older iPod Touches can no longer connect to the app store. What's more, there are probably no apps left on the store that will work with the iOS available on the older iPods.

 Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support