They don't necessarily have highly upturned ends. Some are fairly flat overall, either because there is very little rise to the gunwales at the ends and/or because the decking is raised amidships to the point that the kingplank is horizontal.
Many courting canoes had wide gunwales, sometimes built up with a triangular piece of wood on top of the section between decks to support a cap of mahogany that matched the angle of the decks (see "Bonita" in pics below, and the canoe on the left on the photo of three... this is Bonita's sister). Inside the gunwale was fitted a coaming that either encircled the cockpit (most common), or was flat against the gunwale between decks, and then followed a straight line to the peak of the deck, such that instead of the coaming at the decks forming a semicircle, it formed a triangle. Some courting canoes, however, were simpler, lacking the wider inwale and having a thin flat cap running the length of the canoe like other closed gunwale canoes (see drawing of red canoe below; one of our Arnold canoes and one of our either Robertson or Waltham canoes is built this way).
Paint jobs varied extremely widely, from simple stripes that followed the gunwale line to very fancy styles. Most commonly, the paint job was two-tone, with a solid body color, a wide stripe at the gunwales and following around the curve of the stem, the two separated by a thin stripe of gold (ofter gold leaf) edged in black. Often the gold stripe was highly decorative in the peaks at each end, and the canoe usually had a name (sometimes just letters such as "B-B"; red canoe detail below) in gold or gold leaf on each side of the bow.
Most, but not all, courting canoes had diamond-shaped flagstaff holders, one in each deck, and they supported a nickel-plated brass flagstaff, to which a pennant was attached (see Bonita photo below). These were fancy, probably made at home, and often displayed the name of the canoe.
The addition of a phonograph, pillows, etc. does not in itself make a courting canoe, though these and other items were often added on during the process of courting. In addition to these things, courting canoes were often outfitted with canopies or mosquito netting. These were generally aftermarket items (I've got an original package around here somewhere), and usually they were attached by several brass fittings screwed to the coaming's inner face along the gunwales, usually 3 per side (see detail photo below). Rarely, a canopy may have been attached via vertical rods as were the larger canopies of launches (such as Fay & Bowen), but more often, the canopy was supported by flat spring steels, one end slipped into a fitting on one side of the canoe, the spring steel bent into a semicircle, and the opposite end fitted into the clip on the opposite gunwale. Three of these spring steel hoops provided support for the canopy.
More than you wanted to know, perhaps, but...
M