If my card has a 'deflect opponent must pay 2 to choose me with an ability' can my opponent exhaust his runes, then pay them?

Yes, your opponent can exhaust their runes to generate the resources needed to pay the Deflect cost.

According to Rule 354.1.a, when paying for a spell or ability, the controller can use activated abilities (such as exhausting a rune to add energy or power) to generate the resources required to pay the costs. Since the Deflect cost is a mandatory additional cost (Rule 735.1.d), it must be paid as part of the process of playing the spell or ability.

To summarize the sequence:

1. Your opponent declares they are playing a spell or ability that targets your unit with Deflect.
2. They determine the total cost, which includes the base cost of the spell/ability plus the mandatory Deflect cost.
3. They then use their available resources—including exhausting runes to generate the necessary energy or power—to pay that total cost.

As noted in the game rules, the Power used to pay the Deflect cost can be of any Domain (Rule 735.1.c.1).