The independent Lausanne-based body met in London to hear a BOA appeal against a World Anti-Doping Agency (WADA) ruling that a lifetime ban is illegal. A decision is expected in mid-April.
Under the BOA rule, sprinter Dwain Chambers and cyclist David Millar will miss this year's London Games. WADA rules specify a maximum two-year ban for a first offence.
"I am cautiously optimistic," Moynihan told Sky Sports television outside the BOA's London headquarters. "I think we put a really strong case today on behalf of the athletes.
"Our selection policy is there with overwhelming support from the athletes. That simply says that we will only accept clean athletes, we won't select those who have knowingly cheated clean athletes out of a place on the team.
"We put that very strongly to the tribunal and had great legal representation. Seven and a half hours later I am cautiously optimistic. We couldn't have put a stronger case."
Chambers, who won a bronze medal in the 60 metres at the world indoor championships in Istanbul at the weekend, said he had been trying not to think about the CAS decision.
"I'm just going to train because that's all I know how to do," he said. "I can't try to be a lawyer, I'm not qualified."
However, London Games organising committee chairman Sebastian Coe, also talking to reporters in Istanbul, said Chambers should not be allowed to compete.
"For me this is not anti-Dwain Chambers," Coe said. "I do believe this is actually about the autonomy of sporting organisations to make judgments and byelaws that they think are in the best interest of their sports."
(Reporting by John Mehaffey; Editing by Ed Osmond)
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