Can anyone recommend a script for this purpose?
If you are asking about requests via email, I know it's tempting, but I really don't think you should use a script.
I think one of the things that makes it most effective is when you can speak from your own point of view.
Offer An Easy Solution
If you are notifying them of a broken link, I think it is most effective if you can find out whether the page they are linking to has moved. So then you can give them the URL of the new page, because they are a lot more likely to take action if you say something like, "the link XYZ is broken, but you can easily fist it by linking to the new page here."
If there isn't a new page, then you could instead suggest a page on your site that they should link to instead.
the easier it is for them to fix the problem, the more likely they are to act on it. Show Common Interest
An important thing to do in your email is blending, which means show what you have in common with them, as they will be more amicable to people that they have something in common with them. So if you could say something like, "It is great to find another site that is also trying to promote [subject here] as well." Get Them To "Finish The Job"
research has shown that people are more willing to finish a project that is already started than start a new task. So I always compliment them on taking the time to maintain their site. Frame their efforts along the lines of that they have already put so much work into their site, don't let that hard work go to waste by not updating their site. People will work harder when they can see the light at the end of the tunnel. Be gently persistent:
put your link targets in a spreadsheet with a column for "Date of Last contact" and another column for "Follow Up Again." If they haven't added your site, then email them again and suggest a different link on someone else's site that is relevant, but is not directly competing with your site. Just mention to them, "Hey, I cam across this site and I really liked it, and I thought maybe you would find it interesting too." Then you can remind them about adding a link to your site.
And as wheel said, the harder it is to get a link from a site, the more valuable that link is to you because your competitors will have a hard time getting a link from them, too.
Also, if they don't link out often, you will get a larger slice of the Page Rank pie, as opposed to a site with tons of links, where you will end up getting a smaller slice.
Hope this helps.