Generally I will warn you not to get too excited when Fickle Pickle shows up on our list of plants. I will however point out that while they will not mass produce anything that we are looking for this week, they are your best source for Fossils and seem to supply them as one of their highest drops. Fickle Pickles are also the only plant that can provide both Fossil and Aether - and they can also give you Stone Block which you can Transmute into Fossil.
As important as Fossils are to the crafter's reagent cabinet, only 2 plants can actually produce it. When I grew 10 Fickle Pickles for 30 days, I received 5 Fossils and 3 Stone Block for my effort. Other Reagents that I received that were most certainly welcome were 3 Diamonds and 3 Sunstone. Within 30 days Fickle Pickles did not give me more than 5 of anything that can be harvested from it.
The only other plant that gives Fossils is Burning Snap Dragons. When I grew 10 of these plants for 30 days I only received 4 Fossils. They are rumored to produce Stone Block but I have never gotten any at all from this plant. Other reagents that I harvested from the plant that is worth mentioning include 20 Black Lotus, 4 Diamond, and 22 Scrap Iron. They are also a decent supplier of Killer Tomato, a rank 7 Fire school Pet Snack.
Unless you are looking for Black Lotus, Scrap Iron, or Pet Snacks, I think I would actually have to recommend growing Fickle Pickles in this rare instance. There is also the fact that Fickle Pickles reproduce quickly while Burning Snap Dragons rarely drop more Burning Snap Dragon Seeds. I only received 2 seeds in 30 days. Burning Snap Dragons do give seeds to grow regular Snap Dragons, however. They won't give you Fossils but they can give you Stone Block and more Burning Snap Dragon seeds.
Let's start with Parsley! It is your best source for Aether, hands down. If you are lucky enough to have Ultra King Parsley seeds, I strongly urge you to plant those bad boys. These plants are amazing and provide Aether, Amber, and an assortment of Ultra Pet Snacks during regular harvests. Elder Harvests can supply you with Merle's Whiskers and Amber Dust. These plants also produce an interesting array of Treasure Cards and other Reagents.
If you don't have Ultra King Parsley, plant as many regular King Parsley seeds as you can scrounge up. They are your second best supplier of Aether (I received 10 within 30 days) and can also provide you with some Ultra King Parsley seeds, Amber, Diamonds, and Sunstone.
Deadly Helephant Ears and Evil Magma Peas are tied in our interests for 3rd top producing plant. Both plants gave me 5 Aether when I grew 10 plants for 30 days. They both are also great sources for Mega Pet Snacks. Personally, Deadly Helephant Ears seeds were much easier to come by. I've been growing these for years where I just finally managed to get a decent amount of Evil Magma Peas seeds.
Dishonorable mentions, as far as Aether harvests go, brings us to Fickle Pickles and Maelstrom Snap Dragon. Fickle Pickles gave me only 1 Aether in 30 days. This could be a welcome addition if you are already growing them for Fossils as mentioned above. Maelstrom Snap Dragon is another example of a plant that is rumored to deliver something, but I personally have never received it. I've grown them for 5 cycles, which took 129 days and never saw a single Aether.
Now please keep in mind that my statistics are a jumping point for you. I do not guarantee that you will have the same results that I have had. You could have better luck or you may have worse luck. Honestly, I think you'd need to be very talented to manage to have worse luck though - I've never been particularly lucky. I just aim to provide a realistic outlook as to which plants have higher yields than others when it comes to specific crafting ingredients.