Raising CP

[PONGALLDAYBRO]

you can only really increase you MAX CP through : food buffs, materia, and you get stat increases (ie CP) everytime you level. there is no cordial equivalent for cp, neither could you use a CP cordial (or any potion) during crafting. there are many crafting skills that give you CP while crafting such as tricks of the trade (WVR) or rumination (CRP). you will need less touches to get quality up with higher control, and craftmanship to get more synthesis progress, in turn higher stats of those will essentially require you to need less CP. if you are having trouple crafting something even with just synthesis - no touches - then it might be time to upgrade your gear.

[Lyrinn]

tricks of the trade (WVR)

ToT is ALC.

And to add onto that, you can use the Hasty Touch method (CUL 15) to improve your quality without using any CP. It's riskier than using basic touches, of course, but it's infinitely cheaper with a bit of luck. You can do this until your gear is at the point where you can HQ without relying on HT.