since @Community resurrected this question, i'll pick up a little where hotpaw left off. i'm not gonna run this through MATLAB or Octave (i can never remember which are columns and which are rows).
let $r$ be the resampling ratio. $r>1$ means that your sample rate has increased and you're making the sequence longer because there are more samples. so if you pad a delay of $\tau$ at the beginning of the input $x[n]$, that should result in a delay of $r \cdot \tau$ at the output $y[n]$ (whether $\tau$ is an integer number of samples or not).
now suppose you pad (using concatenation) the input with $P$ samples of zero before $x[0]$. $P$ is a positive integer. that will result in a pad in the resampled output $y[n]$ of $rP$ samples where $rP$ is not necessarily an integer. but
$$ \lfloor rP \rfloor \triangleq \operatorname{floor}(rP) $$
is an integer, and you can strip those samples (which will be mostly zero) off of the beginning of $y[n]$. $\lfloor u \rfloor$ is the most positive integer that is no greater than $u$. this is always the case:
$$ \lfloor u \rfloor \le u < \lfloor u \rfloor + 1 $$
at least for $u \ge 0$, we might say that $\lfloor u \rfloor$ is the "integer part" of $u$. the "fractional part" of $u$ is whatever is left:
$$ 0 \le u - \lfloor u \rfloor < 1 $$
so, if what we want left is a fractional delay of $\alpha$ samples where $0 \le \alpha < 1$, then we want to choose an integer $P$ to pad the input such that $\alpha$ is the fractional part remaining in the output delay after stripping away the integer part, $\lfloor rP \rfloor$. that is, given the sample rate ratio $r$, and fractional delay $\alpha$, we want to choose $P$ such that:
$$ rP = \lfloor rP \rfloor + \alpha $$
or
$$ \alpha = rP - \lfloor rP \rfloor \ . $$
after thinking about this a while, the only algorithm i can suggest is to start with $P=1$ and iteratively increment $P$ so that the above equation is close enough to be accurate. that is, given an error constraint on $\alpha$, (call it $0 < \epsilon \ll 1$), increment $P$ until
$$ \left|\alpha - \left( rP - \lfloor rP \rfloor \right) \right| < \epsilon $$
pad the input with $P$ samples of zero, and strip the output of $\lfloor rP \rfloor$ samples, and you will be left with $\left( rP - \lfloor rP \rfloor \right)$ samples of delay.
