These items aren't exactly arguments, but since you're asking.
* Two video clips, Michele campaigning for his senate race, in each clip she says: "....is Kenyan"
* The publisher's book blurb 'was born in Kenya'
* That Honolulu Advertiser article and that Nairobi newspaper article someone found (they said) by searching Barrack instead of Barack. I dont know who found them. I saw them the day they were put online. The Advertiser article covered him the day he campaigned for Tammy Duckworth in Honolulu. He was quoted, paraphrasing: "America is wonderful because Tammy and I can serve in Congress even though we were not born in this great country." The Nairobi article was celebrating their native son becoming a U S Senator. Maybe fakes, so I immediately checked each paper's website. Both were there at the sites. Seemed legit. Next day I went to see again and both came up "404 not found". Same next day, and I searched their archives, nothing found.
Then they released the birth certificates and that was that.