There are many kinds of wooden, rope-tuned drums the world over. One simple type called an Alfaia is still in use in Northeastern Brazil.
The Alfaia has very few parts: the shell, or main body; two skins or heads, mounted on flesh hoops, two counter hoops (or just 'hoops,') a rope that laces through the counter hoops to hold the drum together and provide tension, and a ring upon which to attach a strap.
Find a reputable, stateside drum maker by simply searching for "Drum Shell." Specify a round bearing edge and a vent hole.
Order an even-numbered diameter for your drum between 16 and 24 inches. The depth or height of the drum is generally equal to the diameter.
Order animal skin heads ready-mounted on flesh hoops. Search for "mounted drum skin."
Finally, pre-drilled counter hoops designed for Alfaias are most reliably available from American makers of Alfaias. To find one, search for "Alfaia California."
Place one hoop on a table. Put one head face down on top of the hoop. Put the shell inside the bottom head, and put the top head face up on the shell. Put the other hoop on top, making sure that holes in the hoops are opposite each other. Secure the whole stack by attaching the bungee cords to the top and bottom hoops, spacing them evenly over the circumference of the drum.
Put the metal ring next to one of the holes in the top hoop, on the inside. Feed about 9 inches of rope through the ring and hole, from the centre of the drum outward. Form a loop around the ring and hoop and tie it securely, leaving about an inch of space between the hoop and the rope loop.
Turn the drum on its side. Pass the free end of the rope through the closest hole in opposite the hoop, always lacing inside to outside. Repeat, one hole at a time, turning as you go, until the drum has a zigzag lacing in all of the holes.
Take up any excess slack.. Pass the end of the rope through the original loop. Pull and hold. Remove the bungee cords.
Pass the end of the rope behind the loop (the 'upper rang') and the next zigzag rang down (the 'lower rang.') Pull the remaining rope all the way through. Pass the end of the rope around the lower rang on the side opposite the loop, and back up underneath the upper rang. Pull rope through, then pull taut, bringing the two rungs next to each other. Pull the rope down toward the next lower rang on the opposite side. This motion will flip the two prior rungs, tightening the head. The flipped rungs become your new top rang.
Repeat with the lower rang on the opposite side. Continue in the same fashion, alternating sides, until you have worked your way all around the drum. Tie a final simple knot, and wrap any excess rope around a set of knots.
Handmade items wrought with natural materials may have a lot of 'character,' e.g. aberrations that require trial and error. Don't worry if your drum doesn't fit together perfectly or easily right away. You can save some time and heartache by purchasing shells stateside, and mounted skins and counterhoops from a luthier who specialises in Alfaias.
It is possible to buy skins and hoops on the Internet at apparently low prices. However, the quality varies so much that many heads simply have to be thrown away and reordered. Most bass drum counter hoops are designed for hardware-tuned drums and are thus unsuitable for rope-tuned drums.