Your fish look in good shape so whatever and however youre feeding them is doing well. They love cucumber, courgette (think that may be known as a zuchinni to most on here) and peas. Ive tried sweetcorn which they loved but didnt seem too good for them and bloated them so woouldnt go there. Apple, bloodworms, live daphnia (from reputable source or you will get parasites), and of course the traditional dried food flakes and sticks/pellets are good as contain good nutrients - just buy it in small tubs and check out the various types that arent too high in protein as they dont need much of it.

A varied diet is good and little more often is best. As in very little 3-4 times a day better than 1 or 2 large feeds. In saying that I only feed mine every other day but lots disagree with me on that one so do your own thing

Goldfish digestive system cannot  absorb foods that are high in complex carbohydrates , such as corn and wheat, so these items will be eaten but passed through the other end pretty much undigested and just pollute the water.  You can feed goldfish food that has high quality protein and plant based fat. These can include worms and other live prey that you can purchase at the pet store to ensure that they do not contain pesticides.

Try giving them some pellets once in a while C: They're easier for the goldfish to catch by the surface and they wouldn't have to swallow as much air as when they're gulping for flakes. But you can keep the flakes as a staple food if you want.
Then I would say that peas are great! Buy a bag of natural frozen peas and thaw them, squeeze them out of their shells and serve them to your fish (: They'll love them for sure! If necessary, cut the pea halves in smaller pieces to fit your goldfish's mouths.
I heard that goldfish love lettuce and zucchini as well, try it out and see how they'll react! You can be quite liberal with the veggies since they're appreciated by, and healthy for, goldfish (:
If they're still pretty small and growing, feed them with some bloodworms or tubifex or other live or freeze dried food. At most twice a week since they can't handle too much of protein It's great for their growth! I noticed on my goldfish that they're getting beautiful deep bodies from them (:

And another thing:
Goldfish don't have stomachs so they can't store any nutrition, therefore it would rather be a waste feeding them a lot once or twice a day. Goldfish need nutrition a few times a day to meet their needs. So feed them at least three times a day but with small amounts of food.
I use to feed mine with staple pellets in the morning and evening and in the mid day I give them a little treat, like peas or bloodworms. Occasionally some color enhancing sinking pellets (They glow so prettily now!)

Thank you all for the feedback, will be trying most of the suggestions, think i'll start with giving them the peas tho.

I'm fairly new to fishkeeping (6months) and every thing seems to be going well, i have had my stock of 3 zebra danios, and 3 fantails since the start, and they are all doing amazing!! (growing by the day). I am finding this site great with getting lots of hints and tips. Although i did not go into fishkeeping lightly, as i researched alot before i got my tank, equiptment and then fish i am still learning new things about then everyday. So once again thanks to all for all posts on various topics, KEEP it up guys!!!

Well i've tried my fish with the peas, i have done everything right i.e, boil them, de-skined them and cut them up into the smallest of pieces, but my fish take it in there mouths then just spit it out again?!?. Surely it cannot be to big for them as it is the smallest i can cut it??? Any1 got any ideas why they would be doing this???
Cheers

I agree that it is probably something new and also to skip a feeding so they are hungrier than usual and then try the peas again.
It's funny my fish are so use to eating what ever i throw in the tanks.  We had steamed shrimp the other night and I threw bits of that in.  we had peas at lunch and I throw that in...they are so excited when they see me walking towards the tank they start swimming wildy like sharks. LOL!

Katarine,
Have you tried a different brand of pellet?
My betta wouldn't eat anything I tried when I first brought him home..I was so frustrated I was ready to take him back to the store before he starved to death..finally I tried one more brand and he Loved it!!  It was by Aqueon betta food....so i ended up buying the goldfish pellets too and they go nuts for them!

Wow! She is picky!!  hopefully your new fish will be less picky and maybe when they eventually are put together she will just eat out of greediness whatever Tiger is being fed!

Mine get a staple diet of goldfish granules and an occasional treat of green leaf lettuce (rinsed well it tap water).  I use a special clip with a suction cup, and take it out after a few hours.  I also hear that tropical fish are fond of broccoli.

Yeah, odd, huh?  When my husband and I went to the zoo and went to see their huge tropical fish exhibit, what did we see but several big stalks of broccoli weighted down for the fishies to nibble on (and nibble they did!). 

i like your ryukin but when choosing a ryukin better to choose a high back.. the higher its back the better..

There's an old-fashioned method that you might find interesting...

Grab a big old glass baking dish (it should be pretty deep, about 4 inches), and put about half an inch of rinsed garden soil in the bottom. Cover with about half an inch of fine gravel (Best to use some from a pre-existing tank) and then carefully fill the dish with water. The soil must be rinsed well, or it will leak tannins into the water and turn it yellow. Then, plant a soft-leaved aquatic plant such as Hemianthus Callitrichoides or another yummy moss or ground cover into the gravel. Put two or three small, hardy fish, such as mosquito fish, into the bowl. Place duckweed or a similar small, floating plant on the surface of the water, and put the dish on a window sill. It shouldn't receive direct sunlight.
Every second day, feed the fish a small pinch of flakes. Some of this will be eaten and some will fall to the bottom of the dish to fertilize the plants.

When the duckweed threatens to cover the surface of the water, toss a pinch or two to the goldies. They love to chase and eat these tiny plants. The same goes for the ground cover, just be sure to rinse off any soil that get caught on the tiny roots, or it will dirty your tank water. The water in the bowl will probably need to be topped up once a week, but other than feeding the small fish and topping up the water, this is a low-maintenance way to provide fresh greens for goldfish.

A small hospital tank, goldfish bowl or wide, low vase can also be used instead of a glass baking dish. They can look quite pretty.