It is possible to add event sources via aws sdk. I faced the same issue and please see code below as the solution using java.
AddPermissionRequest addPermissionRequest = new AddPermissionRequest();
addPermissionRequest.setStatementId("12345ff"); //any unique string would go
addPermissionRequest.withSourceArn(ruleArn); //CloudWatch rule's arn
addPermissionRequest.setAction("lambda:InvokeFunction");
addPermissionRequest.setPrincipal("events.amazonaws.com");
addPermissionRequest.setFunctionName("name of your lambda function");
AWSLambdaAsyncClient lambdaClient = new AWSLambdaAsyncClient();
lambdaClient.withRegion(Regions.US_EAST_1); //region of your lambda's location
lambdaClient.addPermission(addPermissionRequest);
これはうまく動作しますが、問題は「AWSLambdaAsyncClient」が推奨されなくなりました。 – chaitanya