The only way that I can think of would be to create an audit trail report and parse for the state "Deleted". This allows you to set an entity filter for the name, plus you could set the modified date range an the report period to maybe help narrow down the information you would need to parse:
IGeneralDetailReportQuery report = MsgRequest.AppendGeneralDetailReportQueryRq();
report.DisplayReport.SetValue(false);
report.GeneralDetailReportType.SetValue(ENGeneralDetailReportType.gdrtAuditTrail);
report.ReportEntityFilter.ORReportEntityFilter.FullNameList.Add("Customer");
report.ORReportPeriod.ReportPeriod.FromReportDate.SetValue(fromDate);
report.ORReportPeriod.ReportPeriod.ToReportDate.SetValue(toDate);
report.ORReportModifiedDate.ReportModifiedDateRangeFilter.FromReportModifiedDate.SetValue(fromModDate);
report.ORReportModifiedDate.ReportModifiedDateRangeFilter.ToReportModifiedDate.SetValue(toModDate);