Identify your situation with the plight of other workers deserving of tips
People don't tip because they think you need the money. They tip because they understand your employer is not paying you a fair wage and that there is a social contract where customers make up the missing wages based on how much they appreciated your service. Please note that my comments are for the United States. Tipping in other countries is very different.
Some people understand they are expected to tip but will really judge it based on how much they liked you. [Insert off-topic rant here about how awful this is for women in particular who have to please male customers but also for everyone who is judged not just on good service but on how much they have to smile, and look pleasing, and etc.]
Others will tip a minimum amount and add more for exceptional service. These are people who understand that customers must pay workers direct wages on top of what the company is charging them.
In the US, most restaurant goers, for example, know that servers get paid a much smaller minimum wage than the (already small) minimum wage workers in other industries start with. So they know that tips of 15-20% are just part of the cost of eating out.
Most people also know that people providing a service when they run a station within a company (hairdressers, nail technicians, massage therapists) need to be tipped because they are underpaid for their work (much of the money you are charged goes to the employer, not to the worker). On the flip side, the rule (which not everyone knows) is that you do not tip the owner of a business. For example, if someone runs a salon you would not tip her/him for work on your hair but you would tip anyone leasing a chair or directly employed.
For traditional taxi rides, some people tip and some don't. Taxi drivers are sometimes employees and sometimes independent but working with a dispatch company. Most riders round up. If the fare is, say, $13.75, they may hand the driver $15 and tell her/him to keep the change.
And now there is Uber (and Lyft and similar companies). Most people I think assume that you are either paid decent wages or that you keep the majority of what you bring in for rides, just like a traditional taxi driver. I don't know a lot about Uber's pay structure but I know that some drivers make good money and a lot of other drivers do not. I know you're paying for your own vehicle and that you're getting less than a taxi driver does.
So your writing job is to identify yourself less with a taxi driver and more with a restaurant server. Think of it as a marketing campaign. You want to educate people as to how little of their fares actually make it down to you (after your substantial costs). But you can't really do this without Uber coming down on you if they find out (I assume).
Your first research is to crunch the numbers. Not just how much money you want or need but what do Uber (etc) drivers make in general? How do the numbers compare to what servers or hairdressers make before tips? What percentage of their income comes from tips? I think there are already multiple articles on the internet and in the press that do this, so you don't have to start from scratch.
You can then create general signs with a message like "you wouldn't forget to tip your server, don't forget to tip your driver." Maybe some of your fellow drivers would also display them so they look like a campaign and not your personal ask.
Then create a personal sign with a "this is your driver" message. Raddevus' answer has some good suggestions there.
Remember, not all services are tipped ones. It's only those that are underpaid because the employer expects tips to make up the difference. So that is how you need to frame your message.