NASHVILLE, Tenn. (AP) _ Vanderbilt University began a search for a new tennis coach Friday, following an investigation by Athletic Director Roy Kramer that shows two members of the 1980-81 team received payments in violation of NCAA regulations.

Coach John Newman tendered his resignation Thursday night after an hour- long meeting with Kramer.

Kramer said his investigation had revealed that ''supplemental benefits in addition to their athletic scholarships'' were received by two team members.

''There is no evidence that any other individuals associated with the tennis program, since that time, have received any type of illegal supplemental benefits,'' Kramer said in a written statement.

Newman, 46, said he felt his resignation was best for all concerned parties.

He was placed on administrative leave Wednesday when the Nashville Banner reported that one former player, Tim Stewart, admitted he and a teammate had received payments from Newman in 1980-81.

Stewart told the Nashville Banner that he was paid $600 a month by Newman to return to school and participate on the tennis team.

After his career was ended by a knee injury in 1981, Stewart said Newman told him the payments would cease.

''I think it (Newman's resignation) was something that had to be done in the end,'' Stewart said. ''I don't feel sorry for the man. I think he earned it.''

Kramer said his findings and any additional allegations which may be directed to the athletic department in the future, along with corrective action taken by the school, will be fully reported to the NCAA and the Southeastern Conference.

''We have received notification of potential violations from Vanderbilt and will now await a detailed report,'' said NCAA spokesman David Cawood.

Cawood said the NCAA invokes a four-year statute of limitations on incidents involving payments of student-athletes, so it is unlikely Vanderbilt will be penalized.