Pam,
I have 2 recipes for Swedish Meatballs. One calls for allspice and the other doesn't and is almost identical to Steph/MN's recipe. I recall making these years ago for a "Gourmet Club" dinner in Oregon. Unfortunately, I couldn't find that recipe but I am almost positive that it contained nutmeg. When we did these "Gourmet Club" dinners, we tried to research them with cookbooks from the local library pertaining to whatever country the dinner featured. In some cases, their were people from the country we were featuring and they gave their own recipes. I don't recall where that recipe came from. Good luck with whatever recipe you decide is authentic.