I have an HDMI-to-component converter that I'm happy with that I grabbed off of Amazon.

You'll want to use s-video for best quality (component would be better but as your TV lacks it s-video is the next-best option). You'll just have to roll the dice on whatever you can find on Amazon (or eBay, or AliExpress, etc.)

Also, outputting a 16:9 signal from the Fire TV Stick to a 4:3 television is going to result in a distorted aspect ratio with an image that is squished to make the images look unnaturally tall and skinny (unless you have a TV that has a widescreen mode in the menu that will letterbox the image it receives to display it in the proper ratio; my Sony Trinitron does this but it's a feature that didn't exist in older TVs or lower-cost models).