I deal with some toys that were no longer suitable for him to play with.

Is it correct to write "with" at the end of the sentence?

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Mostly, it is correct because it is clear (easy to understand) and concise, and because the "with" is more connected to the meaning of the verb than to whatever word might have followed it.

In English grammar books, students are often told never to end a sentence with a preposition. However, in this usage, the "with" is not functioning as a preposition. It is functioning as part of the verb.

Sometimes, people will try to twist a sentence around and re-word it to move the "with" to another part of the sentence. In your sentence, moving the "with" would make the sentence difficult to understand, and awkward. There are even jokes _about_ sentences changed to keep the word "with" away from the end of the sentence.

(The problem with many grammar books is that they tried to apply Latin grammatical rules to English, which is a Germanic language.)