For example, the Rudrashtakam occurs in the Uttara Kanda of Ramacharitmanas, which is composed by Sri Tulsidasa Goswami, who is a Rama Bhakt. I have heard he praise Lord Shiva several times in the work. Also all the demigods including Lord Sri Krishna himself pray to Lord Shiva in the Srimad Bhaagavatam (compiled by Vyasadeva) to request him to save them from the poison from verse 8.7.21 (https://prabhupadabooks.com/sb/8/7/21) to 8.7.35 (https://prabhupadabooks.com/sb/8/7/35). What are some other prayers devoted to Lord Shiva coming from a Vaishnava source? Please name the source as well.
EDIT : The commenters are telling me to say that questions asking for a list are too broad, so if you can name even one prayer each (along with the source), that will do.