Baking soda/acid is a good system, but it is ultimately fairly expensive. Furthermore, you also release acetate ions/salts, as well as other volatiles from the vinegar (which is not a pure solution of acetic acid, of course). They prolly won't kill your plants, though they might. Instead they will likely make it smell or taste bad.
What is a better way to get your carbon dioxide? Fermentation. Acquire some brewer's yeast if you can. The types of yeast you can use are in order of what is best, though all are acceptable:
Rig up a simple fermentation chamber with airlock. The airlock is designed to keep the atmosphere anaerobic while releasing your good CO2. Fermentation chamber should be any airtight container with top. It could be a 2 liter Coke bottle, for example. Drill a hole in its top and glue in some plastic tubing, making sure to create a good seal. An epoxy is prolly what you'll need to do it. Run that tube into a smaller, halved bottle: a water bottle works well. Place the tube at the exact bottom and glue it there such that the outlet of the tube faces the wall (not the bottom) and is not blocked (by glue, the wall, your mouse, whatever). Fill that up with water, about an inch and a half above the bottom.
The mechanism is all set up, now set up the fermentation. Fill the bottle with about a 20% solution of glucose (dextrose) by mass and place a few tsp. of yeast in that jaunt. Placing the yeast in some warm water for half an hour prior with some sugar is a good way to jump-start the process. Using those six-carboned sugars, you get optimum results, but other sugars can be used. In general, you'll likely find the 5-carbon variety (fructose: corn syrup, eg.) or the polysaccharide (sucrose: cane sugar). In these cases, its ok to add a little more sugar, no more than 25%. Champagne yeast can tolerate more. Brewers yeast, you may want to shoot for less. Cap that jaunt with the tubing/cap system you rigged up.
Here's the principal, its perty simple: The yeast use the sugar to make their energy (ATP). However, in absence of oxygen, the metabolic pathways can't be completed, and alcohol is excreted as waste. This is disadvantageous to the yeast, but hey, who cares? They also release carbon dioxide. For every equivalent of glucose or dextrose, the yeast produces two equivalents of carbon dioxide and alcohol. If other sugars are used, the process is slightly less efficient due to the early metabolics that get done to prepare it, or the inefficiency of metabolic/synthetic shunts (biochemical shite, its unimportant, but fun if you are nerdy). The carbon dioxide is good for your plants: its the objective. The alcohol is bad. It increases in concentration in the fermentation vessle and DOES NOT leave in any way. Over time, the yeast poisons itself with its own waste. Better yeasts (as per the above sheet) survive longer and make more carbon dioxide. Hence the reason for increasing the sugar, if you'd like (the difference is probably just about marginal if at all, so don't dwell on it).
So what does this mean for you? A mole of glucose is around 180 grams. Thus, a 20% mass solution will produce slightly more than TWO MOLES (2.2 to be be exact) of of gas per liter. At standard temperature and pressure, and if you are growing, that's what you want, you will get around 50 liters of pure carbon dioxide from this method, over the time period of about 2-4 weeks. Great stuff.
Problems: You can tell the yeast are dying when the bubbling through the airlock subsides. No way around it, you need to whip up another fermentation mixture. Optimally you would do this every week and a half, while the yeast are at their maximum productivity. Using cane sugar and baker's yeast this is a crazy inexpensive endeavour.
Can you kill the plants with too much CO2? Most likely not. They breathe it as air, and they really only need oxygen (the only other thing they really take from the air) to run their ETC and some other minor metabolic processes. They get this from the water, believe it or not. Also they respirate as much 02 as they take in CO2. No problem, really. Time when killing the plants from carbon dioxide have been reported is likely either in extreme cases (approaching NO oxygen in the air and thus water) or due to the poor downsides to using other carbon producing methods (acidic air, contamination of various sorts, etc.). On the other hand, your plants would optimally have about 3 times as much carbon dioxide as would be in the atmosphere. That rings in at around 6%, so not that much, and in all likelihood, its gonna be difficult to bring it up to these levels. Happy planting.