I have a plastic trophy (of a big tire) that I would like to paint. For the actual tire part of the trophy, it would be cool if it felt like a tire (rubbery).
Is there a type of paint, that when dry, will feel like tire rubber?
A product by the brand name PlastiDip™ exists in spray-on and brush on or dip form. It's somewhat rubbery and is often used as grips for tool handles. Available at the Amazon link in various colors and application types.
I've used it in dip form to encase lead "muffins" to be used as fabric weights, protecting the surfaces from marking and any possibility of hazardous material transfer, but for your tire idea, a well masked hub sprayed with PlastiDip will certainly provide a tire rubber feel. Image from linked site:
Liquid electrical tape will do the job. However it's pretty thick though and globs on so it will be challenging to have the underlying texture not be covered up.
Alternatively, you could try mixing in fine rubber powder filler with regular black paint, resin or whatever. Make sure to do plenty of trials before putting it on your final workpiece.
You could use black liquid latex that is sold as body paint. It is natural latex that you can brush or pour on and it will give you an actual rubber coating. I have played with the stuff and it is a lot of fun, dries pretty fast and is real rubber so will definitely give you the feel of a rubber tire.
Using an acrylic primer as a base layer may help to get it to adhere better and that is also available in black (though the latex is opaque it cannot hurt to match the color). A quick search online shows a variety of brands, often sold as fetish item but also as makeup/fashion product.