A fairly uncommon form of reduplication in words and phrases has an initial unrhymed portion followed by a rhyming pair, of the form ABB.
One syllable repeated:
ajaja (the roseate spoonbill)
aholehole
brouhaha (a disturbance; a fight)
cantata (a kind of musical composition)
Chihuahua (a state in Mexico; a breed of dog)
Kinshasha (capital of the Democratic Republic of the Congo)
pahoehoe (lava that has hardened into ropey forms)
rococo
Waikiki
One syllable rhymed:
ace boon coon (a good friend)
apropos
away day (an off-site meeting; a game held away from a team's home)
awry-eyed (drunk)
bad luck Chuck (an unlucky person)
[the] Bahamas
bandana (a neck or head cloth)
bayou blue (cheap or bootleg whiskey)
Blue Jay Way (a street in Los Angeles's "Bird Streets" neighborhood,
popular with actors, and made famous by a Beatles song of
that name)
conundrum ([approximate rhyme] a puzzle or problem)
Deflategate (a controversy in which quarterback Tom Brady was accused
of using slightly deflated footballs that would improve handling)
Don't Say Gay (a proposed law in Florida which would forbid classroom
discussion of "inappropriate" topics in sexuality, which would be...?)
the divine nine (a nickname for the nine African
American fraternities and sororities)
five jump chump (someone who has made the required number
of jumps to pass parachute training in the Army)
front row joe (a devoted attendee of multiple rallies, always
to be found sitting in the front row)
genome tome (a reference to the compilation of the content
of the human genome)
lambada (a dance)
motel hell (a job, place or relationship that is unbearable)
No Man's Land (in World War I, the extremely dangerous area between
the two opposing armies.)
no clothes pose (a nude photograph)
one man band (a solo performer)
one-stop shop (a place where all that is necessary may
be obtained)
reply guy (a man who compulsively adds his opinion to an
ongoing conversation, whether or not it was invited or topical)
resentment
right hand man (one's closest associate)
severe clear (a pilot's term for seeming infinite visibility)
shoo-fly pie (a Pennsylvania Dutch dessert)
sundown town (a town where blacks were not allowed after dark)
Surreal Neil (the nickname of the lead singer in Super Diamond,
a Neil Diamond tribute band)
surround sound (a very realistic sound system)
Tahiti
Teflon Don (John Gotti's nickname, when no charge would
stick to him; Donald Trump's nickname)
three pump chump (a man who has almost no sexual stamina)
two buck Chuck (the nickname for Charles Shaw wine,
which sells for $1.99 a bottle)
two pump chump (a man who has no sexual stamina)
the Utah Claw (a hairstyle involving upswept bangs)
the vaccine queen (an epithet applied to Hillary Clinton by
anti-vaccination zealots)
Two syllables repeated:
opaka-paka (a snapper fish)
Satanic panic (a hysterical period in the 1980's involving daycare centers
Two syllables rhymed:
Aracataca (a town in Colombia, home to Gabriel Garcia Marquez)
Bahama mama
baloney pony (the penis)
Satanic panic (a wave of accusations about Satanism in the 1970s)
spaghetti Eddy (a nickname for Eddy)
Almost satisfactory:
"Astronomy Domine" (the name of a song on a Pink Floyd album)
nicotine queen (a woman who is a heavy smoker)