This app was mentioned in 5 comments, with an average of 1.40 upvotes
Might not be what you're looking for, but I love Kairosft's management games and they have a couple of farming ones.
I can tell it's a mobile game made by Japanese company dev Kairosoft. They also made Game Dev Story. Unfortunately, I can't really tell which game this is, since they all look similar.
My favorite of their is Dungeon Village.
Edit: It's their newest game, 8-Bit Farm: https://play.google.com/store/apps/details?id=net.kairosoft.android.bokujou_en&referrer=utm_source%3Dkairopark%26utm_medium%3Dhouse_ad%26utm_campaign%3Dtext
This is a great question that I wish I had more games to answer with. Here are a couple that might scratch that itch.
This game is made from Kairosoft, which has a long history of making games in which you run a certain type of job. In this one you are in charge of a farm and have to try to be the best farm there is. Their most well-known game being Game Dev Story, so if you like this style, check it out.
Now this is also another game by Kairosoft but it plays slightly different from the other one. Maybe try the light versions of both to figure out what you prefer the best. Also I suggest maybe looking through /r/Kairosoft to see which they prefer.
This game is similar to some of the Kairosoft games and it takes place in you running your own brewery. Similar to a farming game since you have to brew the right drinks for maximum profit.
Emulators:
Another good option is to use an emulator to play some older games, such as Harvest Moon which is great farming game, maybe do some research online to figure out the best one to emulate since there are a decent amount to choose from.
Sure! I know it's mostly low graded games, but it still exists: <em>many</em> on the Google Play Store with specific emphasis on this one.
Really, it's mostly games that have "retro" or "8 bit" in the title