The existing tires on the three wheeler are:
Avon SM 4.00-19 65H
Max speed: 130mph/210kph
Max weight: 640lbs/290kg
Here are some alternatives. You can Google the names to find sources in your country. They are easy (and cheap) to find online in Europe and the USA. I've used the Heidenau, Duro, and Avon in other applications and they've all been good tires.
Heidenau K34 4.00-19M/C 64H TT
Max Speed: 130mph/210kph
Max weight: 620lbs/280kg
Note: The weight rating is slightly less (10kg/20lbs) than the stock tires.
Avon SAFETY MILEAGE MK2 (Mark II) 4.00-19M/C 65H TT
Max Speed: 130mph/210kph
Max Weight: 640lbs/290kg
Note: Is this what the stock tire is? It is listed as being a "rear" tire.
Duro HF308 72P
Max Speed: 94mph/150kph
Max Weight: 780lbs/355kg
Note: Limited max speed
Mitas H 02 RF 4.00-19M/C 71P TT
Max Speed: 94mph/150kph
Max Weight: 760lbs/345kg
Note: Limited max speed
Use this to decode the meaning of the speed, weight, etc... markings on your tire:
http://en.wikipedia.org/wiki/Tire_code