You can use cider yeast, ale yeast or champagne yeast. Most homebrew shops carry all of these. Dry versions are the easiest to work with, but you can use liquid as well. They are all generally formulated for 5 gal batches, so try to use a little less than half. For dry, you can pour the grains out into a dark bowl and then try to separate, or use a precision scale. If you use too much yeast in a Mr. Beer kit, I've heard they can explode, so maybe go a little under. Dry yeasts are ok to buy online as well. Champagne and dry cider yeast are better for drier cider, but I've heard people have good luck with English ale yeasts too. With liquid yeast there are more varieties to choose from.
If you are making your own fresh cider/juice, you can try doing it without adding any extra yeast if you buy organic apples. Apples have yeast naturally living on their skin, so if you leave the skin on when you extract the juice, there will be enough naturally occurring/wild yeast to ferment the batch. Obviously avoid non-organic/conventional apples if you go this route because of the pesticides.
Also, as an alternative to Mr. Beer, you can get some better equipment quite cheaply. You can buy a 1 gallon glass jug with a rubber stopper and an airlock for about $10 - with an airlock you won't need to worry about the fermenter exploding, as CO2 can escape (unlike in Mr. Beer). You can also get a 3 gallon Better Bottle, which works great for small batches. Additionally, many people make cider and apfelwein right in the plastic container the juice/cider comes in. Just add a rubber stopper and airlock, or drill a hole in the juice bottle cap and add a rubber grommet and airlock. Plastic fermenters and even carboys from homebrew shops are pretty inexpensive in general. Online shops also sell 2 & 5 gal cider kits with buckets or carboys, with less equipment than beer kits. Cider-making requires way less equipment and is way cheaper than making beer!