I try to keep at least 1 gallon of frozen colostrum on hand, our first cow to calve every year has enough milk to feed 4 calves, and she loves grain, so i ususally put her calf on one teat and strip out milk on the other side, she will stand without being tied as long as the grain lasts, fortunately we used be dairy farmers so i got pretty good at milking by hand.
As to colostrum from a neighboring dairy it isn't a good idea as was stated previously due to the differences in antibodies between farms, we found that out the hard way last year, i was out of colostrum and had acalf that wouldn't nurse so we got some colostrum from a big dairy we deal with, but 4 days later the calf was dead due to uncontrollable scours that draxin, exenell, and baytril couldn't cure
milking a cow by hand may be a pain but lossing a calf is worse