The lack of internal structure means that your mid century storage bed needs support throughout its length — it will simply fall through a set of bed gates. No box spring also reduces the airflow below your futon mattress. A good futon frame has slats that allow air to pass through the frame. The simplest futon frames mimic the styles of traditional Japan: a series of spaced slats interlaced over a pair of simple wooden rails.
Sand all surfaces in your wood until they are furniture smooth. Traditional futon frames go unpainted, but if you want to paint, do it before continuing. Place the two beams on their 2-inch edges, lay parallel to each other and approximately 30 inches apart. Set your first slat perpendicular to the beams. Align an edge with a set of ends of the beams. Set the ends of the slat so that they extend evenly on the outer sides of the beams.
Screw the slat into place using a wooden screw per beam. Set the screw at the center of both the slat and the beam, driving the screw through the surface of the slat and at the edge of the beam. Be sure to lower the screw head in the soft pine forest, otherwise you risk getting caught and tearing your futon mattress. Set the next slat in place, parallel to and one inch from the first. You can use the narrow edge of a spare lamella to ensure even spacing. Screw it in place as you did the first. Repeat step five to mount the remaining slats, working until you have covered the entire top edges of the beams.