No. There is nothing in any HTML specification for setting the border color at all, still less on a per-element basis. There is the widely supported nonstandard bordercolor attribute, but it works on the table as a whole, setting all border colors in it.

What comes closest to what you are asking is the trick of wrapping the content of the cell in a single-cell table and setting border color on it:

<table>
<tr>
  <td>foo
  <td><table border=2 rules=none bordercolor=red><tr><td>bar</table>
  <td>more
</table>

The style of the border is then browser-dependent, and so is the visual impression of its color, since solid red looks different from outset red. Moreover, the border is really inside the table cell, not around it, as you see if you set border on the outer table:

<table border=1>
<tr>
  <td>foo
  <td><table border=2 rules=none bordercolor=red><tr><td>bar</table>
  <td>more
</table>

I assume you are doing something horrible like HTML email:

<center><table bgcolor="#ff00ff"></table></center>

This example is working fine on IE8, Chrome 9 and Firefox 3.6 so I really can't see what is the problem.

HTML used in the example:

<table>
    <tr>
        <td>AAA</td>
        <td class="middle">BBB</td>
        <td>CCC</td>
    </tr>
</table>

CSS:

.middle { border: 2px solid blue; }
tr { border: 2px solid red; }

Result: