Has any Avenger been an Avenger-specific creation?

The following Avengers have all had their first appearance in an Avengers comic some on the side of Good some on the side of Evil.

Vision first appeared in Avengers #34

Swordsman (Jacques Duquesne)first appeared in Avengers #19

Black Knight first appeared in Avengers #47. He infiltrated the Masters of Evil to help the Avengers bring them down.

Mantis first appeared in Avengers #112 on the side of good.

Wonder Man first appeared in Avengers #9. Given his powers by Baron Zemo to help him and the Masters of Evil destroy the Avengers.

Jocastafirst appeared in Avengers #162 built as the mate of Ultron by Ultron

Moira Brandon first appeared and died in Avengers: West Coast #100 she owned the West Coast Avengers Mansion

Living Lightning first appeared in Avengers: West Coast #63. He first fought against the West Coast Avengers after first getting his powers and again under the control of Doctor Demonicus.

Ant-Man(Scott Lang) first appeared in Avengers #181, stealing the Ant-Man costume from Henry Pym in an attempt to save his daughter's life from a fatal heart condition.

Ravonna first appeared in Avengers #23 saving the life of Kang the Conqueror because she was in love with him.

Yellowjacket first appeared in Avengers #264 stealing the Yellowjacket costume from Henry Pym.

The majority of the Great Lakes Avengers were either introduced in Great Lakes Avengers #1 or West Coast Avengers Vol. 2 # 46 with the exceptions of Squirrel Girl, Monkey Joe, Tippy Toe (Great Lakes Avengers #5), Deadpool, and Gravity.

Rage first appeared in Avengers #326 demanding entry into the Avengers due to their lack of black members.

Swordsman (Philip Javert) first appeared in Avengers #343 as a member of the Gatherers. He is from Earth-921 and a member of that group of Avengers before the planet was destroyed.

Magdalene first appeared in Avengers #343 as a member of the Gatherers.

Deathcry first appeared in Avengers #343 ordered by Lilandra of the Shi'ar to join the Avengers as protector against the Kree.

3-D Man first appeared in Avengers Vol. 3 #8. He gained his powers from Jonathan Tremont the founder of the Triune Understanding and a wielder of one of three fragments of a mysterious object.

Silverclaw first appeared in Avengers Vol. 3 #8.

Lionheart first appeared in Avengers Vol 3 #77 during a battle between the Avengers and the Wrecking Crew.

Queen Veranke first appeared in New Avengers #1.

The majority of the members of the Young Avengers first appeared in Young Avengers #1 with the exception of Stature(Marvel Premiere #47), Vision(Young Avengers #5), and Speed(Young Avengers #10)

Maria Hill first appeared in New Avengers #4.

For full list of Avengers Members