Do it well and thoroughly. It is more efficient and in the end more beneficial to send appropriate requests to fewer organizations than to send a shower of appeals in the hopes that one may land in the right place. While you may not receive an approval or even a hearing on the first attempt, if the appeal has been well thought out and is indeed within the guidelines of the foundation, the impression left is a positive one and the next time you try, you may be more successful. Obviously, there are no guarantees, and since there are always many more appeals sent than resources to fill the need, a majority are turned down. Once you have determined that you are sending your appeal to an interested party, make sure the form of your approach is correct.
Many foundations prefer a phone call or a letter of inquiry as the first step.
Others want a full proposal with all required documentation. It saves time and paperwork and ultimately will produce more positive than negative results. The relationship between grantee and grantor is mutual. I hope is, more often than not, a relationship of respect and responsibility. It is our responsibility to read and review requests with an open mind, making fair judgments without being judgmental.