You can't make new effects, but you can hijack existing ones. You can give the bound items different meshes and enchantments if you wish. Otherwise you'll need to make scripted spells if you need something more.
Ahh, that's what I feared. But yeah, scripting a new spell seems like the only choice, since I want my bound weapons to be different from the weapons summoned by NPCs and creatures.
Hmm... Interesting question. I'm going to have to look into this.
Post here if you think of something
EDIT: There aren't any mods like this, right? Because if one happened to exist I could just hijack it, hehe.