We would rather they _______ with us tonight.

• শূন্যস্থানে সঠিক উত্তর হবে - stayed
- Complete sentence: We would rather they stayed with us tonight.
-----------------------
• Would rather + same subject + verb base form.
• Would rather + different subject + verb past simple/ past perfect form.
 
• সাধারণত Would rather/ Had better এর পরে Verb এর Present form হয়।
- যেমন
- I would rather die than let you go.
- You had better finish your homework.
- I’d rather stay at home than go out tonight.
 
• কিন্তু subject + would rather এবং এরপর যদি আরেকটি subject আসে, তাহলে verb এর past indefinite অথবা past perfect tense হয়।
• I would rather you + the simple past - is a sentence structure you can use to express your preference about what somebody does in a specific present or future event.
- যেমন -
I’d rather you stayed at home tonight.
I’d rather you didn’t go out tonight.

• আবার, 
•  I would rather you + the past perfect - is a sentence structure that allows you to express your preference over a situation that occurred in the past.
- Example: I would rather you hadn’t called him and told him I was late.
 
• যেহেতু, প্রশ্ন প্রদত্ত বাক্যে, We would rather এরপর দ্বিতীয় subject হিসাবে you এসেছে এবং ভবিষ্যতের কথা নির্দেশ করছে তাই verb এর simple past form হবে।

Source: Cambridge Dictionary.