Like the Subject says- is there any way to do this besides manually entering them into the new phone?

Just received a new iPhone SE today. Have searched online, and there are apps like "Move To iOS" but it looks like they sync with contacts in GMail or other e-mail contact lists, and I don't know if any of these apps search through the telephone number lists. I haven't gotten around to entering all contact info, ie, e-mail and phone # for a person into those e-mail account listings. I tend to keep phone numbers and e-mails separate, and lots of my contacts are phone only, or e-mail only.

What says the hive?

on android you could "send" contacts via bluetooth.
sort of like the business card thing. it allows you to send them all at one time.
see if you can pair the two phones and if the iphone will recieve that.

Is there a SIM card?

There is an option for "copy contacts from sim card" buried somewhere in iOS.

If there is data on the SIM, you might be able to use that.

I always do that stuff manually so I can get rid of numbers I no longer need.