The phrase "peculiar conversation" is correct and can be used in written English.
You can use it when describing an unusual or odd conversation, typically one that stands out from normal or expected conversations. Example: "As they walked into the café, they overheard a peculiar conversation between two customers discussing the merits of conspiracy theories."
"He was always very good in those peculiar Washington conversations in which people try to convince each other how much they really know about what is going on in the government, because he generally did know".
A peculiar kind of conversation takes shape, a bit like what one might overhear at a shotgun wedding -- scattered, oblique and utterly fascinating.
Australia's very Australianness – the peculiar rhythm of conversation and daily life, the energies of a people at once hard, resourceful and aspiring to something better – is so strong, it's impossible not to be influenced by it when you grow up there.
The writer describes his encounter with a pygmy at the Guest House bar in the southern Rwandan hill town of Gikongoro... Writer elaborates on a theme in their conversation: the peculiar necessity of imagining what is in fact real.
Later this year, Ms. Bukey will also introduce her line of peculiar home décor: witty conversation pieces like a fake piano top to turn your table into a party and a one-dimensional fireplace to hang on the wall if your apartment lacks one.
Even more so, however, she was interested in the conversations that the peculiar landmark would inspire ― the gossip, the faulty histories, the myths. .
Without adequate face-to-face conversation, a person grows peculiar.
As you do this, continue your conversation as if nothing peculiar is going on.
As they grown increasingly tired, their conversation takes on a more peculiar and serious tone.
She came up with the idea for the series after having a conversation with friends about how peculiar terms like "trophy wife" really were.
