I don’t see anything wrong with that sentence. It’s similar to saying “It might be possible”. In my opinion, saying “could be possible” is simply less certain or more tentative than “is possible”. In certain situations, it might be used to soften the statement. As is often the case, the context could be very important.
As Amy says, could be possible suggests that there is some kind of reluctance to come out and say it is possible. It’s the sort of answer you give when you are hedging your bets as to the feasibility of something.
You put forward a solution to a problem and the reaction is a tad luke warm as someone says: Yes, it could be possible (underlying is the feeling that they have their doubts). I’ll give it some thought.