As another answer stated - there aren't many [if any] denominations in mainstream Western groups that demarcate themselves or make a statement on hunting, etc...
So, assuming we say that the basic answer to the question is "there aren't denominations that specifically call out hunting" - we can then move to other forms of analyzing why the statement may have been made.
Therefore, OP may also be running into the distinctions between the Regulative and Normative theological interpretation and not necessarily denomination specific distinctives. In fact, there may not by any reason to believe the statement is anything other than a personal belief without more information from OP.
To put it very very simply
One is not to do anything not explicitly commanded in Scripture
One is allowed to do anything not explicitly forbidden in Scripture
So - your friend's statement that there is a 'Biblical basis' for sport hunting could stem from a normative interpretation of the Bible, in that, since it is not expressly mentioned/forbidden, it is allowable.
Additionally, there could be a nearly infinite number of self-identified 'denominations' that it would be impossible to definitely answer the question as stated. With that in mind, we can look at the more well-recognized denominations (as opposed to splinter groups, Westboro-esque, etc...)
Southern Baptist Convention:
no mention of hunting, animals, or environmental management of any kind in the official 2000 Baptist Faith and Message
United Methodist Church:
no mention of hunting, animals, or environmental management of any kind in the Articles of Relgion
Note: UMC does include a note about earthly stewardship in the Social Principles: The Natural World section of their website. However, there is not a specific word on sport hunting one way or the other
(other references coming as I get the time :)