I have implemented a custom datePickerTableCell to show a date picker on cell edit. I am using the ExtFX DatePicker (https://bitbucket.org/sco0ter/extfx/overview). Everything wo
See if this example helps. It uses Java 8 and the DatePicker control from there.
This example may help too. It uses a DatePicker and TableView control with Java 8.
Maybe have a look at this example. It uses a color picker but works as well for a date picker:
public class ColorTableCell<T> extends TableCell<T, Color> {    
    private final ColorPicker colorPicker;
    public ColorTableCell(TableColumn<T, Color> column) {
        this.colorPicker = new ColorPicker();
        this.colorPicker.editableProperty().bind(column.editableProperty());
        this.colorPicker.disableProperty().bind(column.editableProperty().not());
        this.colorPicker.setOnShowing(event -> {
            final TableView<T> tableView = getTableView();
            tableView.getSelectionModel().select(getTableRow().getIndex());
            tableView.edit(tableView.getSelectionModel().getSelectedIndex(), column);       
        });
        this.colorPicker.valueProperty().addListener((observable, oldValue, newValue) -> {
            if(isEditing()) {
                commitEdit(newValue);
            }
        });     
        setContentDisplay(ContentDisplay.GRAPHIC_ONLY);
    }
    @Override
    protected void updateItem(Color item, boolean empty) {
        super.updateItem(item, empty);  
        setText(null);  
        if(empty) {     
            setGraphic(null);
        } else {        
            this.colorPicker.setValue(item);
            this.setGraphic(this.colorPicker);
        } 
    }
}
If you're on Java 7, replace the lambdas with anonymous inner classes, but it should work as well. Full blog post is here.
I faced a similar issue when using a TextArea as table cells. The issue turns out to be I was using startEdit in the TableCell implementation. Using TableView#edit instead of startEdit resolved the issue.