Database
I have made use of the following table Customers with the schema as follows.
I have already inserted few records in the table.
 
You can download database SQL from here.
As you have said that your page is opened all the time then here i have used SetInterval as the timer to check the time whether it is equal to 10 AM or not. If you use Ajax Timer then page will postback each 1 seconds. So i have used SetInterval.
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
        table
        {
            border: 1px solid #ccc;
        }
        table th
        {
            background-color: #F7F7F7;
            color: #333;
            font-weight: bold;
        }
        table th, table td
        {
            padding: 5px;
            border-color: #ccc;
        }
    </style>
    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
    <script type="text/javascript">
        var inter;
        window.onload = function () {
            inter = setInterval(CheckTime, 1000);
        }
        function CheckTime() {
            var hours = new Date().getHours();
            var hours = (hours + 24) % 24;
            var mid = 'AM';
            if (hours == 0) { //At 00 hours we need to show 12 am
                hours = 12;
            }
            else if (hours > 12) {
                hours = hours % 12;
                mid = 'PM';
            }
            var currentTime = hours + ' ' + mid;
            if (currentTime == "9 AM") {
                $('[id*=GridView1] tr:not(:first)').each(function () {
                    var customer = {};
                    customer.CustomerId = $(this).find("td:first").html();
                    customer.Name = $(this).find("td:nth-child(2)").html();
                    customer.Country = $(this).find("td:last").html();
                    $.ajax({
                        type: "POST",
                        url: "Default.aspx/SaveUser",
                        data: '{customer: ' + JSON.stringify(customer) + '}',
                        contentType: "application/json; charset=utf-8",
                        dataType: "json",
                        success: function (response) {
                        }
                    });
                });                
                clearInterval(inter);
            }
        }       
        
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <asp:ScriptManager runat="server" />
        <asp:GridView ID="GridView1" HeaderStyle-BackColor="#3AC0F2" HeaderStyle-ForeColor="White"
            runat="server" AutoGenerateColumns="false">
            <Columns>
                <asp:BoundField DataField="CustomerId" HeaderText="CustomerId" ItemStyle-Width="30" />
                <asp:BoundField DataField="Name" HeaderText="Name" ItemStyle-Width="150" />
                <asp:BoundField DataField="Country" HeaderText="Country" ItemStyle-Width="150" />
            </Columns>
        </asp:GridView>
    </div>
    </form>
</body>
</html>
Namespaces
using System.Data;
using System.Configuration;
using System.Data.SqlClient;
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlConnection con = new SqlConnection(constr))
        {
            using (SqlCommand cmd = new SqlCommand("Select * FROM Customers", con))
            {
                con.Open();
                GridView1.DataSource = cmd.ExecuteReader();
                GridView1.DataBind();
                con.Close();
            }
        }
    }
}
public class Customer
{
    public string CustomerId { get; set; }
    public string Name { get; set; }
    public string Country { get; set; }
}
[System.Web.Services.WebMethod(EnableSession = true)]
[System.Web.Script.Services.ScriptMethod]
public static void SaveUser(Customer customer)
{
    if (HttpContext.Current.Session["Saved"] == null)
    {
        string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlConnection con = new SqlConnection(constr))
        {
            using (SqlCommand cmd = new SqlCommand("INSERT INTO Customers VALUES(@CustomerId, @Name, @Country)"))
            {
                cmd.CommandType = CommandType.Text;
                cmd.Parameters.AddWithValue("@CustomerId", customer.CustomerId);
                cmd.Parameters.AddWithValue("@Name", customer.Name);
                cmd.Parameters.AddWithValue("@Country", customer.Country);
                cmd.Connection = con;
                con.Open();
                cmd.ExecuteNonQuery();
                con.Close();
                HttpContext.Current.Session["Saved"] = true;
                HttpContext.Current.Session.Timeout = 60;
            }
        }
    }
}