Well, glad to see how helpful the folks here are with fellow openvz users.
Anyway, I was able to get this working and it's run the last few days. I'm posting this because I think it may be helpful for others that are looking for a way to stagger backing up larger numbers of VMs on their host nodes.
#!/bin/sh
# How many days per week do you want to run backups? (starts on monday)
DPW=5
####### END OF CONFIGURATION
if [[ $(date +%u) -gt $DPW ]] ; then
echo 'Sorry, you cannot run this program today.'
exit
fi
#figure out how many VMs we have, and figure out how many to backup each day of the week
TOTAL=`/usr/sbin/vzlist -H -o ctid|wc -l`
DAILY=$(($TOTAL/$DPW))
# if Monday, backup first set of $DAILY number of VMs, if tuesday then second set, etc...
DAY="$(date +'%u')"
NUM2=$(($DAILY * $DAY))
NUM1=$((($NUM2 - $DAILY)+1))
if [[ ($DAY -eq $DPW) && ($NUM2 -lt $TOTAL) ]]; then
NUM2=$TOTAL
fi
# Get list of all VMs, remove leading whitespace, segment them and then back them up
for VM in `/usr/sbin/vzlist -H -o ctid | sed 's/^[ \t]*//' | sed -n "$NUM1,$NUM2 p"`; do /usr/sbin/vzdump --suspend $VM --tmpdir /vz/dump/tmp; done