Kombucha Tea is my lifesaver! It's a low sugar, fermented tea that is naturally carbonated (like soda) and contains healthy bacteria and probiotics that help boost your immune system. I have it post dinner to help with digestion and cure my sweet tooth.
It's easy to make your own at home and is a fraction of the cost compared to the store bought kinds. Although, every now and then I treat myself to GT's Kombucha (dark bottle at most Whole Foods) because my home brew doesn't come close.
You should not drink any pop while on the paleo diet, at least until you have given it an honest try for at least a month. If you still want pop after that then just keep it very moderate, even to the point of a once-weekly or once-monthly treat (then you can get a nice Jones soda or similar).
While there may not be evidence pointing to poisonous effects from fake sugar, there is scientific evidence supporting the fact that diet soda causes you to eat more. I'd also point out that there is a significant difference between a study on effects of the sugar substitute by itself vs. a study on the effects of substituting diet coke for water in the diet. I've read many accounts of aspartame causing migraines and other neurological issues (anecdotal of course).
If we're talking about occasionally drinking a pop on the weekends then you have little to worry about, but everyday consumption is going to affect you. Grab an apple, eat a handful of berries, give kombucha tea a try (it is carbonated and low in sugar while still tasting sweet). You should be trying to change your lifestyle, not just to conform to a diet somewhat.
You're going to find people on here that hate diet drinks and artificial sweeteners, so it's probably not the best place to ask that question. Maybe a year ago I might have agreed with them, but to be honest, there is not sufficient experimental evidence to substantiate claims that aspartame and sucralose are harmful in any way. I know there are other artificial sweeteners but these are the ones which I have researched and looked into.
In the case of aspartame, you are already consuming it as it is nothing more than a dipeptide (a two amino acid molecule) of the amino acids aspartic acid and phenylalanine. These two amino acids occur naturally in almost all foods that you eat, including meats, eggs, seafood, nuts, fruits, vegetables, etc. Your stomach breaks down proteins into amino acids during digestion, it does the same thing with aspartame, by breaking it down into its constituent amino acids.
In the case of sucralose, has been thoroughly tested for toxicity and carcinogenicity many, many times and continually found to be perfectly safe and tolerable in even the highest of doses. Here is further reading if you're interested: http://www.fda.gov/ohrms/dockets/98fr/040398a.pdf
My suggestion would be to do your research. Many times people will utilize fear (for lack of scientific evidence) in order to get you to go in a certain direction, and since we are human and have emotions which are often illogical, we allow fear to take over our reasoning. If you absolutely must have something sweet, you're probably better off with diet drinks than with something sugary like juice and certainly better off than with regular soda.
Drinks that are allowed in Paleo Diet are:
1. The bulk of liquid consumption in Paleo Diet should be plain water.
2. In Paleo Diet, small amounts of wine are acceptable
3. Herbal tea especially green tea is permitted on the Paleo Diet.
Drinks that are not recommended while following Paleo Diet:
1. Soda and energy drinks aren't permitted.
2. Fruit juice is a tricky drink
3. The entire dairy group is also off limits on the Paleo Diet
Definitely no diet soft drinks. They are full of chemicals (that I personally think they'll discover to be harmful in the future) and the sweet taste messes up your metabolism even if there is no sugar.
Tea can be ok but can have a lot of caffeine, which can be ok for a bit but you don't want to be having it all day.
I would just get in the habit of drinking a lot of water.
I recommend... tea, water, soda water w/ lime or kombucha (brew your own).... all of these are a lot better & cheaper than diet soda. Soda water by the bottle can be spendy but consider a SodaStream and make your own bubbly water for a LOT less.
Google the history of diet soda, very interesting but kinda scary chemistry to be drinking.