Depending on how hands on you want to get, you can buy a tyre online, or shop around and find a good price, then fit it yourself using plastic garden stakes to roll the tyre over the rim.
Balancing on bikes is static balancing, i.e. you put the axle on two blocks, make it perfectly level, then spin it and see where it stops, mark it with chalk, spin it again. If it stops at the same place, bluetak in place a small weight on the opposite side of the rim. Keep doing this until the point it stops at starts to randomize.