I've only had a few minutes, so this may not work first time - you might have to tweak the code a bit - but this should display the immediate subcategories of the current category/subcategory.
Code:
{if $printable ne ''}
{include file="customer/tab_menu_printable.tpl"}
{else}
<TABLE width="100%" border="0" cellpadding="0" cellspacing="0">
<TR><TD align="center">
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR>
{if $cat eq 0}
<TD align="center" class="tabmenuitemon" nowrap>
<span>home</span>
</TD>
{else}
<TD align="center" class="tabmenuitem" nowrap>
<span>home</span>
</TD>
{/if}
{section name=cat_num loop=$categories}
{if $categories[cat_num].order_by lt 10}
{if $cat eq $categories[cat_num].categoryid || $current_category.parentid eq $categories[cat_num].categoryid}
<TD align="center" class="tabmenuitemon" nowrap>
<span>{$categories[cat_num].category}</span>
</TD>
{else}
<TD align="center" class="tabmenuitem" nowrap>
<span>{$categories[cat_num].category}</span>
</TD>
{/if}
{/if}
{/section}
</TR>
</TABLE>
</TD></TR>
<TR><TD class="submenu" align="center" valign="top">
<TABLE border="0" cellpadding="0" cellspacing="0">
{assign var=current_category_top value=$current_category.categoryid_path|regex_replace:"/\/.*/":""}
<TR>
<TD class="submenuitem"></TD>
{if $cat gt 0}
{assign var=subcat_count value=1}
{section name=sub_num loop=$allcategories}
{if $allcategories[sub_num].categoryid eq $cat || $allcategories[sub_num].categoryid eq $current_category.parentid}
<TD class="submenuitemon" align="center" nowrap>
{$allcategories[sub_num].category|truncate:20:"...":true}{if $subcat_count eq 7 || $subcat_count eq 14 || $subcat_count eq 21}</TD></TR></TABLE><TABLE border="0" cellpadding="0" cellspacing="0"><TR><TD class="submenuitem">{elseif not %sub_num.last%}<FONT class="submenuitem">|</FONT>{/if}</TD>
{assign var=subcat_count value=$subcat_count+1}
{/if}
{/section}
{else}
<TD class="submenumsg" align="center" valign="middle">{$lng.lbl_welcome_msg}</TD>
{/if}
<TD class="submenuitem"></TD>
</TR>
</TABLE>
</TD></TR>
</TABLE>
{/if}