I swear, finding the newest 'Aurora Teagarden Mysteries' movies feels like its own cozy mystery sometimes. The most reliable spot I've found is Hallmark Movies & Mysteries. They've got exclusive rights to the original ones, so they premiere there first and then usually end up available on their streaming app. I think it's part of a bigger subscription now called Frndly TV? Something like that. It's a bit of a pain because it's not on the massive platforms, but the upside is they air them pretty consistently in batches, like a whole 'whodunnit weekend' sort of thing.
If you miss the linear broadcast, check the Hallmark Movies Now streaming service. They rotate the library, so newer ones pop up a few months after they air on TV. I haven't had much luck with the big names like Netflix or Hulu for the latest ones, though. They sometimes have older seasons, but it's spotty. A slightly grayer area is buying individual episodes on digital stores like Amazon Prime Video, Vudu, or Apple TV—they're usually available to purchase the day after the TV premiere if you're desperate and don't want to subscribe to another service. I caved and bought the last one because I couldn't wait; it's not ideal, but it gets the job done.
Honestly, the whole ecosystem for these Hallmark mystery series is its own niche. It's a bit old-fashioned in how it's distributed, which kinda fits the show's vibe. Just be prepared to either time your viewing with their TV schedule or accept that you might need a specific app or purchase to catch Aurora's latest small-town sleuthing adventure right away.