Rock&Roll, my first guess is that your water pump is OK, at least if you don't have leakage out of the weap hole, and or the pump is not squealing. So what the other guys have advised is good advice. However if you do want to buy a new pump, perhaps you might want to check out Rockauto.com. They list a 59tbird 352 water pump for $67. You can check out their advertisement in the "Parts for Sale" catagory of this Squarebirds.org user forum and find Rock Auto's ad that gives 5% off.
'58HT and '48 Dodge Panel in MN
Thunderbird Registry #3810 VTCI#7652