Well, I did look into that

. Cannon were used on the battlefield -admittedly to very little effect- at Sekigahara. Here Mitsunari ordered five cannon to fire at the attacking Tokugawa troops. They didn´t hit much, but managed to drive them back, which is -in my experience- about what good stonethrowers have ever done me on the gaming table
But apart from that cannon may be used in sieges and there were a lot of sieges in the Sengoku period. So we need cannon!
As for the stonethrower/cannon comparison. As I understand it Japanese (or borrowed Western) cannon fired large metal balls of fixed diameter or, in case of Japanese-made ordnance, weight. Not unlike stones, I think. They were pretty inaccurate, but like stonethrowers fired their missiles in a high trajectory and had enough range to overshoot the invulnerable walls of castles and reach the wooden structures within, which was where their real effect lay. The balls were capable of destroying these structures and sometimes setting them alight. Also ST have a long, but limited range. I think it´s bad form to introduce artillery that may fire across the whole table.
Personally I didn´t think the comparison with a ST was a bad one. Admittedly I never read ECW, which might have better cannon rules (and contemporary at that) but so far so good. But Geert will borrow me his ECW to study, so I´m open to better alternatives.
Finally, the ninja. Well, you have me there. Ninja took part in several battles (more battles than featured cannon, anyway

) but AFAIK mainly as disguised or stealthy insurgents into camps and besieged castles and sometimes as ambushers and traplayers on battlefields. The first role I find hard to emulate in general rules, although I see the scenario potential. For the second role I imagine a kind of stealthy Ulfhednar with a skill like Concealment from AoArt. But their appearance was also extremely rare and I wouldn´t want to see them pop up in every army because they´re cool... OTOH that might be none of my business. What about this?
0-1 unit of Ninja
M Ws Bs S T W I A Ld Pts
4 4 4 3 3 1 4 1 7 30
Hand weapon. May take light armour (+1), samurai sword (+2), throwing knives (+1, treat as javelin), thrusting spear (+1), Bow (+2), naginata (+2), teppo (2) or musket (+3). Stubborn. Concealment. Light Infantry.
Ninja may be chosen as allies in the early Muromachi and both the Sengoku periods.
Optional rules: Ninja may lay in ambush somewhere on the table. Their position is drawn on a map. The unit is not placed on the table before the ninja come into action or are spotted. The opponent may request to see the map then. A ninja unit is spotted as an enemy unit passes its position within 4". Ninja may also disguise themselves and as such enter the table looking like another unit. The ninja unit is only placed on the table as soon as they reveal themselves.