How about...

class StoreMember extends Model
{
    public function visits()
    {
        return $this->hasMany('Visits', 'user_id', 'user_id')
            ->where('store_id', $this->store_id);
    }

Hey @Neoglyph, thanks for the reply. Unfortunately I don't think this works when eager loading the relationship. With the proposed method, if you lazy load like this it works:

$storeMember = StoreMember::where('user_id',1)->where('store_id',1)->first();
dd($storeMember->visits);

However, if you eager load like this it doesn't work:

$storeMember = StoreMember::with('visits')->where('user_id',1)->where('store_id',1)->first();
dd($storeMember->visits);

I think its because at the time the relationship is processed $this->store_id is null when eager loading. It seems like there should be a way to define multiple indexes for the relationship, not just one. Taylor seems pretty opposed to supporting composite keys for some reason. I'll just stick with my single primary key for the time being I guess. Thanks again.

Use Compoships to add support for multi-columns relationship in Laravel 5's Eloquent: https://github.com/topclaudy/compoships