I want to start this off by letting you know that this is certainly not the most comprehensive list of all the pens that are out there. In fact, I really just want to tell you about the two types that I regularly use, and love!
Firstly, lets talk about what works on vinyl stickers. Gel pens don't, won't, don't even bother trying. They just smear everywhere. Vinyl has a very different surface to paper stickers and ink can't absorb in like it does on paper. So vinyl needs pens don't rely on ink soaking in to work. This leaves us with...drum roll please... permanent markers. Thankfully, gone are the days when they only come in black, blue and red, and with a really huge tip. Now they come in a range of beautiful colours and super fine tips - perfect for our planner needs! I've tried a few different brands, and although there was none that I disliked, I have now stuck to the Sharpie Ultra Fine Permanent Markers.
They are a good price on Amazon or your local office supplies store, and they seem to be bringing out more and more ranges of colours. They write perfectly on the vinyl - both the matte and glossy vinyl, with super rich ink. I'd just be a little cautious writing directly into your planner with these pens however. Depending on the thickness of the paper in your planner, they could bleed through to the other side.
Enter, my second type of pen I use nearly ever day. For beautiful colours and a pleasure to write with, I can't go past the Staedtler Triplus Fineliner. Available to buy individually or in packs with heaps of lovely colours! Also, easy to find online or in stores for purchase. Between these two types of pens, I am pretty set! Plenty of colour and they are just a joy to use. I will mention also, some biros will work on vinyl if you get stuck. Give it time to dry, however. It wont look anywhere near as rich as permanent marker, but will get you out of trouble.
For those who are new to planning or new to vinyl, I hope this was helpful. If you have a favourite pen I haven't mentioned here, comment below to share with others!