What kitchen foods are best for my hand-fed baby canary's diet?

The easies solution is either Recovery from Royal canin or a/d from hills, both are wet foods designed for cats and dogs but are suitable for baby birds as well, you can draw them into a syringe and feed this bird (many times a day!)

Offer a fortified seed mix supplemented with cooked beans and vegetables (carrots, peas, etc). Fresh water should be available at all times. A mineral block and/or cuttlebone should also be placed in the cage. Keep the room at a steady temp and keep the cage away from strong drafts. You can mist him with warm water a few times weekly to promote preening and healthy plumage. Monitor for lethargy, decreased appetite and loose droppings. If necessary, have him physically examined by your veterinarian or an experienced avian veterinarian.

There are various recipes available online, usually these are based on products such as cereals for human babies, peanut butter, apple sauce and baby food (e.g. https://www.cuteness.com/article/make-homemade-baby-cockatiel-food). I cannot really recommend those, perhaps only as a last resort. If you can get commercial pellets for adult parrots and grind them with water (pre-boiled) to prepare a slurry, that would work, but the commercial formulae are better. Please note that the food should be at 40-41C and prepared fresh for each feeding.

Is the female coming out of the nest to feed? You can try offering food closer to her nest. Are you sure she is sitting and not ill and hiding? Try offering different foods that might be more enticing (grated carrots, alfalfa sprouts, millet, etc.) Good luck.

You could but it would not be a balanced diet. A commercial handfeeding formula would provide complete nutrition for your growing chick. You can purchase it at most pet stores or online. If you can't find one, a better recipe can be found online using your preferred search engine. Follow the link for an example. http://www.indianringneck.com/forum/viewtopic.php

You can definitely try to feed it, you will need to buy wet canned cat food such as Recovery or A/D (from your local vet) as well as a syringe, you will need to feed it every couple hours during the day (no need to feed during the night).

...without first speaking to a veterinarian since hand feeding babies can be tricky and possibly even lethal if you are not doing it correctly. If you cannot find a commercial formula, try the following recipe: -3 tablespoons of high protien baby cereal -1 1/2 tablespoons of wheat germ -1 1/2 tablespoons of millet meal -1 1/2 tablespoons of sunflower meal -5 drops of a multivitamin for birds. Blend all ingredients to a fine powder and then mix with warm water to a soupy consistency.