I think the biggest problem with a 19 is that it just isn't that big of a boat. Plus, there are the issues of the mainsheet getting in the way, if you tried to stow it rolled up facing aft. Stowed facing forward, there would be the issues of the companionway and vang, potentially. It all depends on the geometries involved. I think you'd have to get the measuring tape out and do some serious thinking.
As suggested above, it might just be easier to rig a tarp. On my 192, I tried to use PCV electrical conduit, because it has sockets molded in, and I could use them to make 2 piece poles. I put one at the stern, and one about 2/3rds forward, going transverse across the boat. This allowed for more room sitting in the cockpit. I also have an adjustable topping lift that allows me to raise the boom up at an angle, and provide standing headroom towards the back of the cockpit. For the forward edge of the tarp, I tied it to the base of the more forward stanchions, so that it dipped down over the cabin top. This allowed me to have a rain cover and keep the companionway open during rain. It significantly increased living area, knowing you could go in and out of the cabin with impunity during rain.
This year, I bought an ultralight backpacking tarp, which I have not tried to rig yet. It won't provide as much sun shade (kinda translucent,) but will take up far less room than the bulky polytarp. The PVC poles assumed a bent shape during a warm day last year, so I'm considering aluminum tent poles this year. I have to rig and measure the new tarp, so there might be some re-thinking this weekend if I try to work it out. Also, I'm considering if a better pole pattern would be to go on diagonals from corner to corner with the poles crossed.
Finally, one of these days, I should really decide what I like best, and then make a custom tarp from old sails I have. The way, I could cut the sides with a concavity, and probably get the works to set better considering wind. Or, just say "chuck it" and go sailing
Apparently, I have a few pictures of the tarp rigged with just one PVC pole. This was from the July 4th flag parade and raft up, which I spent the majority of the afternoon in the water. It was hot that day! You can see that I tried to attach the tarp to the pole using S hooks. I think I abandoned that in favor of holes drilled into the PVC, and tied directly to the tarp. As old Gwen (who was at the raft up) said, "Awww, look how sweet, playing with your pre-bimini! Don't get offended, we ALL did it, before we finally invest in a real bimini." Hahaha!
