I don't think you'll be able to get a definitive answer (there's no set criteria for who gets to appear on US currency) but there are some aspects about John Adams that makes him a less-than-ideal candidate for appearing on currency:

• He wasn't especially popular with his contemporaries. He served only one term as president before being defeated in the next election. He often butted heads with his colleagues and was not very tact: rather he is perhaps best known for his gaffs, such as when he attempted to title the president as His Highness, which eventually led to his nickname of "His Rotundity".
• He was controversial. Aside from the above, he is also well known for signing into law the Alien and Sedition Acts, which was a very divisive piece of legislation even for its own time.
• He didn't have one singular big "thing" to set him apart. John Adams accomplished a lot of stuff, but he arguably didn't have a grand achievement like writing the Declaration of Independence, or serving as Commander-in-Chief of the Continental Army. Most people who end up on widely-circulated US currency are really well-known for one or two big things.

He actually did appear on the back of the $100 state bank note issued by North Carolina, along with the other signers of Declaration of Independence, and the image was based on a famous painting by John Trumbull. (That's Mr. Adams in the center.) They stopped allowing the practice of states printing their own currency back in 1935.

Technically he is on the presidential dollar coin and the 2$ bill.