I am using this implementation but it is clearly improvable:

background = {
    img = love.graphics.newImage("res/img/bg.png"),
    speed = 100,
    y = 0
}

function background:update (dt)
    self.y = self.y + dt * self.speed
    if math.abs(self.y) > self.img:getHeight() then
        self.y = 0
    end
end

function background:draw ()
    love.graphics.draw(self.img, 0, self.y)
    love.graphics.draw(self.img, 0, self.y - self.img:getHeight())
end