I’m not sure how you were searching, but if you Google “Catholic prayer hotline” you will get a bunch of results. Many such hotlines are run by religious orders; others are run by groups of churches. Some sites also take your prayer requests by e-mail or through a web form. There are like 10 results on the first search results page alone. And many more on Page 2, Page 3, Page 4 etc.
In addition to the ones that come up on Google, I’m aware of other ones locally that print their number in Church bulletins and such. The Sisters of St. Joseph in my hometown had a prayer line and when you call, either you got an answering machine to leave a message, or sometimes a sister actually answers. You give them your intention and they pray for you.
I would further note that virtually every Catholic shrine or religious order at the very least has a webpage where you can submit, often anonymously, a prayer request via the web.
EWTN, Catholic World Missions and other Catholic organizations also have online web forms for you to submit an intention for prayer. If you do a Google search on “Catholic prayer request” or “Catholic prayer intention” you will get a bunch of these sites.