hands down, the best newborn diaper cover is a pair of fleece pants. even massive "newborn sized" fleece pants such as the ones dear hudson is modeling. we've got a TON of different diaper covers. all are too big on this little peanut. i recall having the same issue with lucy as well--covers intended for babies sized 6-13 pounds are simply too bulky on a 7 pound baby. they irritate the cord stump, and the velcro closure makes a sounds that can be jarring to a startle-prone newborn.
enter a simple pair of fleece pants. wool is also amazing and serves a similar purpose--the 2 pairs of wool longies that we have in our stash are just too big for hudson at the moment (whose thighs are seriously 3 inches in circumference). but wool is generally not machine-washable, and it's easy to just toss fleece pants into the wash at the end of the day. so i dug up a pair of fleece pants i got at a thrift store awhile back. my mom also gave us a pair as part of a gift. they're PERFECT for comfort, warmth, and keeping leaks at bay. plus, no added bulk. a few pairs should be on the "too buy" list of every cloth-diapering mama to be!