Are there any divination systems or tools that come from your tradition? Are there any methods from other traditions you've adapted into your practices?
It can be a bit weird to think about it in this way because contemporary Paganism is reconstructive. What does it mean to conclude something is from "our" traditions versus "their" traditions? Are these delineations important or meaningful, and if so, in what way and why?
For the most part I concern myself less with those types of questions and more with "can this tradition be adapted in an appropriate and respectful way into my practice?" and then "how do I then make this mine so I connect with it deeply and meaningfully?"
Many years ago, I did this process with runes. A mentor encouraged selecting one of the different futhark and ritually crafting a set. Then, instead of using canned meanings we were to commune with each rune. In this way we developed deeply personal connections with each symbol and in effect crafted our own system of divination with the runes. This same intuitive process is encouraged in various mystery schools as well, and if you put the work and the time in it's a fantastic method.
Consequentially, one could say the runes "come from" an outsider's tradition (I am not any stripe of Nordic-inspired Pagan) but also "come from" my own because I made it my own.
It can be hard to know how to word things when one is still half asleep...
(There wasn't enough activity for my liking upon waking, so I created some of my own...)
I do like the personal process you mention here, that you went through with your runes. I think being able to bond with your tool or method is an important aspect on whether or not you will be successful with it.
I think one struggle I've had with tarot is that the images feel 'severe', and a little alien. Any time I've tried to get into it(because I like the idea of it), I end up stepping back sooner or later because I feel uncomfortable with it. Last night, I ran across a Hindu oriented deck which I'm considering. Looking at the card images that were shown, I found much more 'warmth' and familiarity radiating from it than most of the other decks I've encountered. Its true, tarot doesn't belong to the Hindu system, but here is an example of something being made meaningful cross tradition.
Many use astrology (whether the Indian, Western, or Chinese version), regardless of what path they're on.
I think my favorite divination tool is the I-Ching, even though it doesn't come from my tradition. I think it was first presented to me when I was in my early 20s. It was easy to learn, but most of all, I liked the 'kindness' that emanated from it. A book that spoke like a friend... to this day, I get chills thinking about the time I consulted it with tears streaming down my face, and it said "do not cry; be like the sun at mid-day".