Aisliyna already mentioned why mutations aren't exactly man made, but I'll try to explain it a little further. (All though I managed to get myself in a very shaky buss again.
Mutations occur in the wild all the time, even color mutations (note that there are many other mutations too... for example the shape of our ears is possibly caused byt multiple different mutations in certain genes). Most of them don't survive for many reasons as the parents may not feed an odd looking baby or predators will catch it because it doesn't blend into the backround as it should. Or no partner will take it. So there are multiple reasons why a bird wouldn't get any offspring to pass the gene on.
Humans are able to intervene in many ways. We only need a succesful mating from the birds and we can do the rest (all though there are even cases of artificial insemination in budgies, but it was for research, not establishing mutations). We can also play a huge part when birds are choosing their mates, because we can limit the possibilities and even alter breeding hormones by simulating certain contidions in the wild. And once we find out the inheritation pattern of a certain gene, we usually do all we can to pass it on. Many mutations are established with inbreeding for several generations, which doesn't happen in a wild, 3000 budgie flock that easily. Inbreeding also increases the possibility for new mutations to show up (both good and bad, so this is no way a suggestion for anyone to try it out).
And as Aisliyna said, making yellow areas greeen or blue isn't possible. Red is also not an option since budgies just don't have red pigments in them. Greyface and black might be possible with some sort of melanistic mutation, but what I've read and seen about melanistic birds, white parts usually seem to stay white, so I'm not sure if grey is possible. I must admit that melanism is a bit outside my genetic knowledge... But even with these, the mutation has to happen before we humans can do anything about it and even then sometimes we just don't manage to keep it.
There is a blackfaced mutation in budgies though, where the barring covers the birds whole face and most of the body, but it hasn't been established yet. That with antracite would produce a very dark bird, nearly black probably.