I've got one iPod touch, but two iTunes accounts on two separate computers When I first joined iTunes (just a month or two ago) I made a new Apple ID and iTunes account.  My sister had an Apple ID/iTunes account that my mother, sister, and brother used for their devices, but I, not ever having owned an iPod, figured that I could make my own iTunes account so that when I do purchase an iPod, I won't be pestering my sister (the first one in our house to have an iPod) for her Apple ID info.  (She's recently left for college and I didn't want to be dependent on her.)

So, I made an account and made use of $65 worth of gift cards that I had sitting around and put them onto my account. Now, my little sister wants some of the songs I've purchased.  But when I go to sync her device on my iTunes library, it tells me syncing will erase everything she has on her device and replace it with my library. I don't want that--I just want to share the songs from my iTunes account with her! 

Is there any sort of solution or correction?
The issue isn't really iTunes accounts, but rather the syncing — you can only sync an iPod or iOS device with one library at a time.

The easiest solution now that iTunes songs are DRM-free is to copy your songs to her library, and then sync her device to her own library. To locate the actual files, select what you want in iTunes, right click and choose Reveal in Finder.