If you want to increase your CYA and chlorine levels simultaneously you can use Dichlor where for every 1 ppm FC you add, you also add 0.9 ppm CYA. It dissolves quickly (unlike CYA and Trichlor tabs) and is not as acidic as Trichlor (though it's still acidic after chlorine gets used up). Just be sure to not add too much as you want SOME CYA, but not too much (even 10 ppm will help, but keep it under 30 ppm total). Getting some CYA in your pool will help keep the FC level consistent during the day, but as Carl says you need to shock consistently in order to get ahead of the algae growth.

In your situation, it sounds like the lack of CYA prevents you from maintaining chlorine levels so the algae is growing faster than the chlorine can kill it off. Essentially, it's as if you are battling two creatures simultaneously -- algae and sunlight. By getting some CYA in your pool, you can prevent sunlight from interfering with your battle against the algae.

Richard