Non-aligned artifacts can be obtained through quests offered by the Knights Guilds.  There are seven artifacts available through two or three quests.  Which artifact you get is determined by the luck of the dice at the time the quest is offered.  Some of the artifacts (Staff of Magnus, for example) have never been obtained by any players that I am aware of (much to the dismay of the artifact collectors).  Two of the artifacts (Warlock's Ring and Necromancer's Amulet) can be obtained merely by giving the Totem of Tiber Septim to Lady Brisienna or to the Underking's agent, respectively.  Of course it's a bit late in the game by that point in time.

Since there is no Daedra to summon, it is possible to own multiple copies of these artifacts.  Considering the general instability of the game platform, it might be wise to not press your luck.  The artifacts are:

Auriel's Bow
Auriel's Shield
Lord's Mail
Necromancer's Amulet
Staff of Magnus
Warlock's Ring