What is a reasonable amount to give as a wedding gift?

It depends on the giver…...there are no rules.

I usually set my limit at 50.00 for all things: weddings, graduations, showers. It depends on your budget.

I’m with @chyna. I’ve got shopping at discount glass stores and bought $100 to $125 marked glass items for $ 50 or less.
Like a crystal glass martini pitcher I gave to a close friend, his MIL took a look at it and wanted to meet me.

We usually stick with $50/head unless it’s realy close family.

Then it could be $100 to $200/head.

Since you have very little contact with your cousine and you are trying to rebuild the lost contact, then a gift worth an above average amount will be a good idea. Based on the above answers, taking the average value of a gift to be around $50–75, I would suggest a gift of worth $100 would be appropriate.
This is just a suggestion to look good and in no way is to be considered as a bribe to rebuild relations. There is no alternative to love, but looking good/generous is not harmful at all.

The price of a good toaster should be enough.

Thanks all. One more question, who do I make the check out to? To Mr and Mrs? Just to my cousin’s daughter. If so, do I use her maiden name or married name?

I made mine out to my cousin, in her maiden name and in the memo section I put both of their names.