Marbles deal 51 damage, the equivalent of a Tentacle Spike. But the damage output per second is equivalent to boomerang due to slingshot's slow attack speed.
10 of them can be crafted for 1 Marble and require an Alchemy Engine to prototype.
Poop Pellets deal no damage, but they force mobs other than Bosses to lose aggro on their target. 10 of them can be crafted for 1 Manure and require a Science Machine to prototype.
Freeze Rounds deal no damage, but they freeze the target equivalent to two hits from an Ice Staff. 10 of them can be crafted for 1 Moon Rock and 1 Blue Gem and require a Prestihatitator to prototype.
Slow-Down Rounds deal 17 damage, the same as pebbles, and slow down the target's movement speed by a third for 30 seconds. 10 of them can be crafted for 1 Moon Rock and 1 Purple Gem and require a Shadow Manipulator to prototype.
The shadow tentacles will deal 34 damage every 2 seconds for 9 seconds per tentacle. Assuming a perfectly stationary enemy (most are not) and that every 2nd shot summons a tentacle, and given the Trusty Slingshot's 0.9 second / shot; on average, we can expect:
Second
0.9
1.8
2.7
3.6
4.5
5.4
6.3
7.2
8.1
9
9.9
10.8
11.7
Shot damage
51
51
51
51
51
51
51
51
51
51
51
51
51
# Tentacles
0
1
1
2
2
3
3
4
4
5
5
5
5
Tentacle damage
0
34
0
68
0
102
0
136
0
170
0
170
0
Total damage
51
86
51
121
51
156
51
191
51
226
51
226
51
After 9 or 10 seconds, the tentacles will die off as fast as they are recreated, so average total damage every other second will not exceed 226. In a 10+ second fight with a stationary enemy, Walter could theoretically approach an average damage of 138 per second (on par with the dark sword). In practice, the slingshot's delay before the first shot after moving, or taking a hit, often means Walter has trouble getting shots off.
This example that treats 0.9 seconds of the slingshot as a whole second for the tentacle for simplicity of calculations, so figures are rough.