Quite simply, you don't.
There are COUNTLESS amounts of furries in the exact same position as you, I'll even waver that a majority of furries are in the position of "I want a fursuit but can't afford one". So if you really wanted donations, you'd have to convince people of a few things
1. You deserve a fursuit more than they deserve a fursuit
2. Getting a fursuit is of a great importance to you
3. Them donating to you will somehow work in their favour.
You can convince people with 2, but 1 and 3 is very, very difficult to convince people of. You either need a WHOLE lot of friends (essentially, be a popufur) or have a very convincing argument, I can't actually imagine any argument that'd convince me to donate to a cause like that. So quite simply, there's a very low chance you'll get money to buy a fursuit through donations.
BUT, luckily, there are alternatives. Most people will pay money in exchange for services, in real life this would be essentially, a job, or doing odd jobs around the house for your parents or neighbours. On the internet however, there are a few better ways to make money. For one, furries love art, if you can draw art, and draw art relatively well, you can probably get some commissions in through that way. Convincing people to commission you if your art is sub-par will be difficult, but a cheap commission price (like $3 to start with) might lure some more people in. If you write you might be able to make money off that too, if you have particular voice talents you can try voice acting for furries with pet-projects or so forth.
You can even make money through games if you play enough. For games like TF2 or Eve Online there's a lot of methods to make [some] money by manipulating the in game economy. Doing so you need to know a lot about how that system works, I don't know so you'd need to ask others. If you happen to play a MMO game a hell-of-a-lot and have lots of items, you might be able to sell items to people via real currency. These ways are slow but better than nothing