the programmer works with AT89C51/ AT89C52 /AT89C55.
So I think it should work with the at89c4051 chip ..because this is a part of the at89c51 group, is this correct?
The one thing that varies the most widely among derivatives is the programming algorithm.
Any kitchen table programmer I have seen (described) is severaly limited in the number of chips it can handle.
If I rememeber correct there is a 4051 variand with ISP, why not just use that one.

Erik