You can set categories checkbox dynamically and checked by default.

With the following markup;

    <SearchEngine:SearchBox ID="SearchBox1" runat="server"></SearchEngine:SearchBox>

    <SearchEngineP:SearchBoxOptions ID="SearchBoxOptions1" runat="server" SearchBoxId="SearchBox1" Locations="" AutoGenerateContentCheckBoxes=false AutoGenerateLocationDropDown=false>

    </SearchEngineP:SearchBoxOptions>

you can do this in codebehind

    protected void Page_Load(object sender, EventArgs e)

    {

        SearchBoxOptions1.Contents.Add(new Keyoti.SearchEngine.Web.Design.StringItem("c1"));

        SearchBoxOptions1.Contents.Add(new Keyoti.SearchEngine.Web.Design.StringItem("c2"));

        (SearchBoxOptions1.ContentCheckBoxes.Controls[0] as CheckBox).Checked = true;

    }

this will add c1 and c2 content option check boxes and check the first checkbox (c1).