When we were raising a conure from hatch we used a peanut butter slurry for this reason, high protein and fat via syringe. I can gather what we used when I get home as post it - that was 5 or 6 years ago now. Little fucker is just fine.

@Cure this is what my wife sent me when i asked if she recalled what we did:

"https://www.prettybird.com/products/19-8-handrearing-formula

99% sure this is the one I used. Note: I was feeding a parrot. I don't know how different this is from what's needed for other bird types.

The PB addition is optional, but gives extra fat. Use a natural PB if you want to have PB as an additive. It doesn't require much, but it definitely helps them put on weight faster.

You want the temperature to be a little above room. Just above lukewarm. Similar to the water temp for waking up yeast in water - 100-105. Do NOT get too hot, err on the side of cool because water too hot can seriously burn them.

You can use a syringe, but I find those dixie paper cups to be ideal. Mix it in there, then pinch to get a pour spout, and carefully feed that way. Toss the cup when you're done. There is a point at which the crop is full, and you'll want to stop then - it can take a while to get a feel for it. The younger and smaller they are, the more frequently they will need to feed, but also the smaller amounts. I found at least half of what I tried to feed wound up on the bird rather than in them, which is probably par for the course in feeding any baby. Be prepared with some wet paper towels to try and wipe them down a bit so it doesn't crust on them.

No need to toilet them - baby birds do that on their own.

Depending on the species, there should be some online info on how often to feed.

They usually will sort of wean themselves. After a while they just don't want you to feed them anymore and want to eat on their own. So be sure once they're getting feathers to also offer them normal, solid bird food in their enclosure."

Hope this helps!